Hi guys, happy vlogmas day 14. Isn't it crazy that like it's already vlogmas day 14? I am quickly getting ready because I'm doing the annual photo with a Disney character. I did do this but I guess like the picture expired or something so my parents are like we have to redo it so Valerie and I are going to Animal Kingdom. I'm honestly like not gonna probably do a hot job on the makeup but I'm just gonna do something light. I went to school and like yo today started out a little rough because we had this like pop quiz on the muscles and literally like what we studied obviously wasn't on it so everyone was like kind of freaking out and I think we all like kind of feel that so at least I got the Lena elbow right like I know that because I remember that for me to see it so that was good obviously and what else did I remember? Oh the inguinal ligament and don't ask me how I remember that stuff but I just do so I was happy that I remember that obviously and I literally just guessed because like I had learned it before and you can really tell I'm rushing this makeup because I don't have a lot of time I think my mom must leave around three even though Valerie is doing something so it might not be exactly three but you know what we're trying here it would be a lot easier if I just got my eyebrows done you know like professionally but it's kind of expensive so like I don't want to be doing that especially given the fact that like I don't have a job right now also two guys like during the day my throat started hurting and I'm like oh crap because like you know when your throat starts hurting it's not good and I have an air appointment on Saturday and everything so I don't know I'm hoping that it'll just like go away there was this like sweet syrupy smell in my classroom I'm like oh maybe that's the reason why my throat's hurting but it's one girl in class like she was kind of like copying a lot so I'm like oh my gosh please please dear god don't let me be sick because yeah no I just don't blame that energy I am not sick not sick not sick it's just my throat hurts a little bit also too this isn't a bad thing but there were some like people in another classroom they're like we're coming up on like Christmas break and like they were asking for like more work to do because I guess one of them is going out of town and I'm like wow that's amazing like even though I do don't get me wrong like I love the medical field I'm so interested in science I love it it's one my like you know it's something that I genuinely like but like you know I don't like it that much to ask for more work so I was like wow talk about like overachiever and typically like people would probably consider me an overachiever but I'm like not at that level like that is like way overachiever so anyway this is so hard to do like fast so I'm just going to speed up this clip that you're watching now because I'm not gonna stop talking cuz it as you guys know like it is hard to like multitask and like concentrate on something especially like when you're trying to hurry so start the time lapse now but you're not Valerie tell the vlog am I all pretty I don't know the vlog can tell you anyway this is my outfit so my outfit okay okay yeah so I'm wearing this because we're going to Animal Kingdom and Valerie got me this shirt and I'm gonna wear my belt bag because the belt bags in this year so I might as well you know and do that and then I did it just some light makeup Valerie give your outfit I have on a white lands in button-down shirt that I've had for years yes and I have jeans that are too big for me because I have lost about 40 pounds since January 1st yes so which is about right 40 pounds in a year yeah but the thing is I haven't replaced my clothes so I threw away all my skinny clothes okay don't wear gave him away yeah she don't need so yeah do we like the mirror I love the mirror look at me okay okay I think we're ready all right okay got a little update on the clubhouse area what little update there's some cement finally get some action yes yes I just thought I would update the vlog all right so we're almost to Animal Kingdom now right Valerie oh she's had her hearing aids in so she can't see I can't hear she can see don't worry she's driving but anyway we're heading to Animal Kingdom we're almost there obviously sorry for the wind it's the air conditioner it has been forever since we've ridden the tram and this camera battery is gonna die shoot you have another one maybe you didn't know well we did that whole announcement thing so it was yeah it was that uh that iridescent evening oh is that what we did yeah so I'm gonna get my picture with a daisy duck right donald duck here in dinoland and then we're gonna get the picture and everything cuz it's the annual picture I've already told you guys that so yeah got the picture all right so Valerie's gonna get her dinosaur kit right all of these are the same right yeah yeah I know some family members watch the videos so I can't show the other things you got okay tell us what we're doing now about we're gonna go buy some tickets so that we can win a cement a source yes our goal is to win the cement a source we are our goal is to win one of those cement a source so I can't vlog cuz no one's here to hold the camera and it's gonna be jumping everywhere so wish us luck for dinner Valerie and I came here those are yours I'll take I'll take the bag but we got guys because that's just a Valerie and Alex type of thing to do right Valerie that's right so Valerie got her usual burger and I got the dog am I getting these no those are mine okay these are yours I know but you know I won't eat all these yeah I know did they make it right now they made a right oh yeah perfect yes okay so I'm home now and I studied the instruments I always say that okay I studied the neurosurgical instruments and I will say those were super hard to learn because there's just so many wrong doors I mean a wrong door is kind of it looks like a plier if I'm like being honest it's like you do this and then like happens the what you need to like clamp or whatever that was a really bad way of explaining it but anyway I'm trying to like explain it in you know layman's terms so you guys can understand there's a lot of names a lot of like things to remember which is fine but I think I know them pretty well at least for like the test purposes and everything I studied that I got up vlogmas day 13 so that's good I'm always so nervous that I'm like gonna miss it or like just because I post late you know I like to have a routine obviously yeah I got up vlogmas day 13 and I met another person he is like one of my mom's managers and he was saying that he works with big influencers as well and so that's like the second person this week that I talked to you about like social media and everything so I'm like you know what even though I'm kind of stagnant like that just reiterates that like I need to keep going and like just keep posting I don't know I will say it's like really hard and stuff to stay motivated but like honestly not really cuz I like doing this and I honestly do it for fun so I can't complain I don't want to put this out there but I guess I'm putting it out there when I say this I'm feeling a little under the weather which really sucks because we're about to go and break and I really don't want to be sick on break knock on wood it's not like code symptoms it's more like cold flu not flu but cold symptoms so it kind of sucks but it's fine this one girl in class she was kind of like coughing a lot so me and like two other classmates feel a little under the weather I mean I can't speak for them but that's what they kind of like said in text messages so I'm like okay maybe hopefully it's not me but like still it sucks it sucks that like I feel this way knock on wood too like I haven't been sick in a while so just like feeling this come on is just really sucks and yeah I wish I would just go away I took a vitamin C pill so I'm like yes I need all the immunity I can get like fight whatever is in me but anyway yeah um I think that is gonna be it for this vlog I hope you guys enjoyed it it was kind of fun kind of different I wish I could do a little bit more different things I try to make the videos a little different hopefully you guys like the little tips and tricks on studying by yourself that I just posted hope you guys enjoyed that too if you guys enjoyed this video make sure to give a thumbs up don't forget to subscribe to my channel I'll see you guys in my next video


So this morning, I saw a title on one of my contemporaries pages, how absence plays with a man's emotions. Is that what playing with ends emotions? And I thought, actually, I could relate to this on a number of levels. Also, I appreciate his assertions that, and I'll just get to the quick on it, that absence can trigger anxiety within a person. And within that anxiety, they actually begin to want to lean forward to a person. And when they begin to lean forward, they tend to forget all the, say, bad things that might be happening in the relationship because they're operating from a place of gratitude that this person is back in their life. So I want you to think about this for a moment where you've been in a relationship with someone and all of a sudden they've taken space from you. What happens to you sometimes is that might create anxiety within you. And you're going to want to have this desire for closeness. So the idea is if you take space from a guy and he's feeling this anxiety, he will want to get closer to you. But is really this really the case all the time? Because certainly if you are in a relationship with a person who is emotionally constipated, emotionally unavailable, maybe he has an avoidant attachment style. And we're going to talk about attachment styles in a moment. Is he necessarily going to feel the same things you might feel? Now I share this with you because I think one of the reasons why I can relate to my clients so well is because I have what's known as an anxious attachment style. And if you're not familiar with the book Attached by Amir Levine and Rachel Heller, I highly recommend reading this to learn the three primary love attachment styles. And within these three primary love attachment styles, there's variations within, but there's anxious, avoidant, and secure. Anxious, avoidant, and secure. And so I happen to have an anxious attachment style, meaning I get needy in relationship. It's kind of funny because I jokingly, my girlfriend I jokingly say she's the guy in the relationship and I'm the chick in the relationship because of this anxious attachment style. Now, let me share this with you. I have been working on healing this for a very long time in my life. And so if my anxious behavior used to be like an eight, nine or 10, now it's probably a two, three or four. I still feel it.  And it certainly can trigger my emotions. And so when there is space between myself and my partner, if there's just a disconnect, it can trigger a lot of stuff within me. So it's kind of interesting because this totally plays into this title. Right now, my girlfriend has taken a trip to Africa. She had a 13 hour flight to get to one spot and another five hour flight to get to another spot. So literally it's taken a day and we have had absence. We have had time apart. Now what's interesting is, and I think you're going to find this really interesting couple things. First off, I'm actually appreciating the space apart because I will tell you that first off, I'm in a long distance relationship and quite frankly in a very short period of time that long distance is going to be shrunk because she is moving out here to Los Angeles. And that's within a five month period of us meeting for the first time. But, you know, and we've spent concentrated time together and then time apart and during the time apart, I'll be candid with you. Getting on the phone every evening to connect has felt like a chore. It's really felt like a chore and the reason why I'm aware of this is right now because of this absence that we have, this space we have. I'm actually appreciating that in the evening, I don't feel this pressure of getting on the phone with somebody and don't get me wrong. I really appreciate getting on the phone with her. I really appreciate connecting with her.  Did you have a good day? I hope you had a good day versus what happens when we're physically together. We're doing things together. We're going out. We're meeting with friends. We're meeting with family. I really, I think men tend to appreciate experiences more than talking on the telephone. In fact, I did a video about why how men don't necessarily bond on the phone. So this time apart has given me kind of a break, which I appreciate and my emotions aren't going through the roof because I feel more secure in this relationship. Now, why I'm sharing this with you, I think it's really critically important to lean into a feeling of being of a secure attachment style. I forgot to mention when I mentioned the book attached, the three primary attachment styles are anxious, avoidant and secure. Anxious, avoidant and secure. Anxious of those people that freak out during space. Avoidance, freak out when there's too much closeness. And secures are like, look, I'm going with the flow because I trust this relationship is going to work out. So it's interesting how I feel a sense of calm during this absence, if you will. Now, let's rewind a few weeks ago after one of our visits. And when she returned back to her home, I felt a disconnect from her. Now, this wasn't physical absence. I began to feeling a disconnect, like because we were so lovey-dovey during our last visit here in Los Angeles. And then after that, I felt a disconnect from her. And that triggered all of my stuff. It triggered all of my wounds of abandonment. Primarily because my mother, bless her soul, she did the best she could as a mom. My mom had a habit of giving love and taking away and giving love and taking away and giving love and taking away. And what I mean is whenever she got angry at my father, my brother, my sister, myself, she would go stone cold in the household. She would literally for about 72 hours just literally go stone cold. Now for her, that was her way of regulating her emotions whenever she got triggered. But I want you to imagine a 4-year-old, a 5-year-old, 10-year-old, 12-year-old boy having their mom emotionally disappear, even though she was physically there, she would emotionally disappear. All her lovingness or kindness. And as a little boy, that triggered my fear of not being good enough, not being lovable, not being likable. In fact, I'm wearing the t-shirt Self-Love Club and it reminds me of my book that I wrote.  A journey of personal development, self-open spiritual work. By the way, there's a link below to get my books in the description. What I'm sharing this with you is I've spent a tremendous amount of time, hours and therapy working on this stuff between my mother and myself. And I have plenty of father issues too. I've done the Hoffman process, I've done Insight, and I only share this with you is to heal the anxious or avoid an attachment style, requires some effort, requires making effort into wanting to learning how to regulate one's emotions. So I was sharing with you how I felt a disconnect between the two of us. I could feel like maybe she was pulling away or at least that was the thought in my mind she was pulling away emotionally from the relationship. Even though we had made plans that she's moving out here, I felt like, is this really going to happen? All of my anxiety started to play with my emotions. Now, I could have behaved in the immature way of trying to fix it, trying to fix it, trying to fix it, trying to fix it, trying to fix it. And when I say immature way, it's because it's the little kid inside of me saying, Mommy, love me, Mommy, love me, Mommy, love me. I had to learn to manage my emotions internally. This isn't easy work, folks. It takes a tremendous amount of self-discipline to regulate one's emotions. This is why I continually recommend book after book after book after book. Now, what's interesting is we ended up having a conversation of what was coming up for her. And she had, this was several weeks back before she was leaving for a trip to Africa, is it she had to plan the trip? There were so many details to take care of. There was all of her own anxiety was coming up about the trip, malaria pills and visas and this thing and I mean just a lot of stuff. And then also planning for the move. So her head space was focused on that. Now, while I'm sharing my personal experience because I jokingly said, I'm the chicken, the relationship, she's the guy, my suspicion, the same thing happens within men. What I mean to say is you've experienced a guy who's got a lot on his plate and it triggers all of your anxiety and such. This is why I come back and I really recommend reading this book, recommend reading this book so you can learn how to regulate your emotions. Because this idea of intentionally taking space to activate a man's insecurities and maybe he'll come back in a place of appreciation may or may not work. I don't suggest playing games with another person. What I do recommend is being more intentional in the process of getting to know one another. Folks, I feel like the reason why my relationship is working is because first we began on a foundation of radical honesty and we laid our cards on the table. I'm going to repeat that radical honesty and we laid our cards on the table. It starts by understanding emotional intimacy. This is why I recommend the book by Robert Masters, emotional intimacy. Folks, you're all craving that relationship where a guy really bonds with you. I get it. You're craving for that. Well, guess what? Men don't know how to create that bond. Men focus on sex and they do focus on being with someone that feels good with it. Listen, when I say focus on it, we're hyper focused on sex. It just is. I'm going to say I'm a horny guy. I'm hyper focused on sex. But also because I want a committed relationship with, I take the actions of wanting to spend regular time with a person. A man who genuinely cares about you is going to invest time in you.  And lastly, he's going to step up in an area of commitment. And what I mean to say, he's going to desire commitment with you. This idea that you can play games to mess with a guy's emotions might temporarily work on a person who might be emotionally constipated, emotionally frustrated and it may not work. I'm not recommend you play this game.  More importantly, I want you to understand what happens internally within you when you're feeling this. And this is why I'm a big proponent of establishing early on some a framework of how your relation. If you're going to listen, if you're going to have sex with a guy, you have every right to establish some set of agreement, some set of parameters, some set of standards for the relationship. This is why if you ever watch my channel, I say. Before you ever have sex with a guy, read chapter one of the book, eight dates by doctors, John and Julie Gottman may invite him to read it to it's about trust and commitment.  But that old adage why buy the cow if you can get the milk for free, which really means is today sleeping with someone is so much easier than it was in the past. And there requires little or no investment other than just saying I want a relationship. Ladies, when you're on a date with a guy first date, and he says he wants a relationship and you say me to you go oh you're on the same page but are you really on the same page? Because if you're like me, you want a relationship where you spend three or four days and nights a week together doing shared activities, hobbies, mutual interest, spending time with family and friends, traveling together, teamwork, building skills, both in your personal and your professional life, intimacy, both physical and emotional intimacy leading to either moving in together or getting married. That's a relationship. It's one type of relationship.  Understanding the context between the two of you is hugely important to determine if the two of you have potential for a serious relationship and I'm going to assume all of you watching this want a serious relationship. This is why if you watch my channel, I habitually recommend book after book after book so you can be better prepared because folks, I know you love the idea of just sitting in your feminine energy and letting a guy claim you. It just seems so great. If he doesn't know what he's doing, how can he even claim you if he doesn't even desire commitment, how can he even claim you. And by the way, you don't want to be claimed anyway. You would like to be partnered with someone I'm assuming. This is why I continually say you are in charge of your relationship destiny and I'm man. It's sadly women give their power away to men. This is why I habitually now recommend the book. I don't love all of the book but a good chunk of it. The book is why men love bitches and bitches stands for babe in total control of herself. Yes. And yet women give their power away to men habitually. Let me share you ways women give their power away. Here's some notes on it. The relationship is on him his terms you abandon your standards and boundaries. You're afraid to speak your truth with him. When the relationship ends all you do is focus on him instead of yourself. You're waiting for him to initiate contact for that need of validation.  After meeting a man you feel like you can't live without him. And you think this other person is the only person in the entire universe that you'll have chemistry with. Those are just some examples how I habitually see women give their power away. Folks if you want to land a quality guy I really highly recommend you change your approach. And when I say a quality guy I merely mean a guy who's going to show up intentional. He's going to desire commitment. And he's going to want to pursue you beyond the surface. By the way one of the things I do as a dating relationship coach. Is to help you learn how to determine which guys are serious versus which guys are going to waste your time. In fact there's a link below to schedule a free discovery call with me to see if working with the coach is right for you. And while I share this with you I just want to share with you something personal here for a moment. That's how I feel like my girlfriend landed me if you're interested in this. First and foremost she started with a quality representation of herself by the way we met on match.com. Also she was on millionaire match to she had a quality representation 30 great photographs of her doing what she loves which is traveling. Thankfully she won't have to post these Africa pictures because she's in a relationship with me quality representation herself. She made herself available easy to connect with and meet she wasn't difficult she wasn't always busy she was very easy to connect with. She was open to exploring a relationship making time to actually want to be and I can see so many women don't make time for a relationship certainly guys don't make time for a relationship. Number four she's not attached to the outcome meaning. I'm not responsible for her happiness she didn't give her power away to me in fact that non attachment might seem like what we're talking about she's the guy and I'm the girl in the relationship. Number four she loves her life and she strives to be her best she lives life on a love based version of life and not a fear based version of life. She's grateful for all the blessings in her life and lastly she showed me her little kid that weird side of her that makes me really appreciate her because here's the thing about absence. But I'm learning while she's gone. I just seem to be appreciating her more and more I appreciate what we have. I'm not on the dating apps swiping looking for someone while we're apart. I'm appreciating this person that's the emotion you want to have triggered is when there is absence is to lean into appreciation from a healthy perspective. But folks and if you're not able to achieve that secure relationship as talked about in the book. Attached you're going to have a problematic relationship. So this is why I'm a big proponent as I said before start with radical honesty laying your cards on the table and learn emotional intimacy together because that's going to build the deep roots of trust between the two of you. Some of the ways to build that trust as I said earlier is social activities hobbies mutual interest and spending time with family and friends. Those are the the this is throughout history how the real deep roots of a relationship are formed when you're physically together on a regular basis. And so when you're apart you don't have to freak out because you built a secure attachment with a person and not an anxious attachment with a person. And so while I appreciate the fact that we all listen this is a work in progress. Okay, this is not I don't think healing is ever final until maybe moments before you pass away. This is a work in process. And I invite you to lean into your own emotions. So you don't get so chaotic in your life, but more importantly, choose a better partner right from the get go. And that's where my help and support can come in. Is this resonating with you? Is this content resonating with you? Please let me know. If it did, please hit that thumbs up. Please share this video. Please subscribe to my channel if you feel like this is making a difference. And I think this would be a good place to wrap up. All right. So I'm going to wrap up as I always do.  I'm going to reach into the camera and give you a hug of love if that's okay. I'm going to ask you to turn to someone at that. That'd be very pillow and give it or them a hug of love. Here's a teddy bear because hugs are a great source of love. And let's face it, we could all use more love in our lives. Thanks a bunch. Bye bye now. Bye bye.


So complex number is what we are going to start today Okay, this is actually a new chapter to most of you complex numbers Right complex number is a chapter which is not taught in any of the boards early I don't think so even in IG curriculum. I think mother will be the best person to tell me on that Why are you exposed to are you exposed to complex numbers? No Right, so this is a new concept for all of us and It is one of the most I would say feared chapter for a 11th grader Now for various reasons number one. Yeah, of course, you do not have any prior exposure to it, right?  Okay Second thing is it's a multifaceted concept multifaceted means it will have a lot of aspects Which come from other chapters? For example, it will have some touches of trigonometry It will have some touches of coordinate geometry. It will have some touches of vectors So because so many concepts help you to solve a complex number problem. Sometimes it makes the concept tricky also Some somebody says that it should make our life easy because you can use the multiple concepts from other vertical of mass to Solve complex number problem. I agree. So both pros and cons are there. It makes life easy. Sometimes it makes life simple difficult also sometimes Now first of all, why do we need a complex number? Okay, what was the need for a complex number? So as you all know Invention basically is an outcome of a necessity Right necessity is an invention is the mother of all invention, right? Hello everyone. Hello. Good evening Okay class started at six, sorry three forty five So when we when we were hunters or when we were primitive man when we were food food gatherers or seed gatherers or hunters We only required natural numbers, right? So our quest for numbers were You know taken care by natural numbers, right? One two three four By the way, natural number itself is defined in different ways in different country You would be surprised to know that in some countries zero is also a part of natural number, okay? Anyway, so why does call natural number because it came very naturally to man, right?  He will never say one point two five one point three six He will never count those kind of numbers But slowly man started doing some kind of barter system, okay? So from food gatherers we started living the life of you know small traders So, let's say I am a trader. I gave let's say Anurag five mangoes, okay? So I will say I have five he will use a natural number to denote that pipe But let's say I take away that five mangoes from him. How will he denote? How many mangoes he's left with if you're using natural numbers at that point of time You will not have any number to denote that you are left with no mangoes or zero mangoes So zero was put into the system and then zero was put into the system people thought that their quest for Numbers was complete or they had a whole set of numbers with them. That's why they started calling it as whole numbers The word whole was because they thought they do not need any number at all They have whole numbers all the numbers I have in my world, okay? But soon they were proven wrong when they started doing a little bit more business when lending and borrowing started happening So let's say I gave Anurag five mangoes and I demanded from him seven mangoes Okay, of course Anurag has to borrow from someone. Let's say a person who has you know mangoes to lend to an Iraq So he will borrow two mangoes and give it to me along with the five he already has So, how do you show the concept of? Oh, I can't So I can't show the more mangoes up. So let's say I know I borrow two mangoes from Akash and he gives it to me. So how does Anurag show the fact that he has borrowed two mangoes? Okay, so it's your negative two and because it's negative two basically man needed integers So whole numbers again, it was bettered by the use of integers. Okay. I'm just drawing another circle Okay Okay Now man started doing farming. Okay, so man went into farming. So let's say Anurag again our Hero of the situation.  Two meter square is not even the size of the bed. I'm sitting on So, let's say two meter square land he had and Anurag had three sons, okay So when I know I was becoming old these three sons demanded that you should divide the land equally among us Right because we are your natural hair of your land. So how will he divide or how much? Land should he give to each of his son? Of course, now, you know the answer now You know that he should give two-third meter square to each one of each of his sons But do you think when integers were known this number two-third was no Correct. So man needed a number like this and therefore he started talking about Rational numbers. So let's make another circle like this. Sorry for a crooked circle. Okay So he required rational numbers like q stands for quotient because you are taking one number divided by the other and The word rational also has come from the word ratio ratio ratio of P by Q. So as you can see, it's a P by Q type of a number Okay, now, let's say the same piece of land Anurag wants to protect firms trespasses, right? He doesn't want anybody to enter his or encroach upon his piece of land So he goes to a person who sells barbed wires.  Now, you know, the answer is four root two Because root two etc is known to us now that time when let's say irrational numbers were not into picture third was not into picture How else would he you know explain how much barbed wire he needed? So he needed something called irrational numbers. So there was another let's say, you know circle I'll draw a small circle, which is Q compliment Q compliment means other than other than rational numbers Now when he got all these numbers, he started calling all these numbers as real numbers Why real because He could signify any real quantity around him by the use of these numbers whether it was the farm size Whether it was the size of the, you know barbed wire he needed any length any dimension He could signify by the use of these numbers. So they were used to Signify real things which he had around us. Okay, but so he ends, you know, gradually man started solving equations and One day Anurag While he was solving equation, he stumbled upon this. Okay, which made him, you know Think very hard that how can how can we have a number? Especially a real number whose square is going to give me a minus one. So he was unable to solve such questions. Okay I'm just giving a funny example. However, this was not the real, you know in Incident that happened it basically happened with the Italian guy called Gary Lamo Cardano Cardano was a guy who was attempting to solve cubic equation Just like quadratic equation, there's a formula He was trying to come up with a cubic equation formula and in the attempt to solve a cubic equation Cardano started, you know stumbled upon these kind of scenario. Okay, not a similar one But not a same one, but a similar one. Okay, so there he started pondering that I need to have a number Whose square will give me a negative answer and there and there he felt the need of Imaginary numbers there he felt the need of imaginary numbers now this word imaginary did not come very you can say on an ad hoc basis Imaginary the word I basically was chosen by Euler Euler was a Swiss mathematician who basically gave this word But before that it was called latent numbers and all those stuff before they finally Decided that they are going to choose the word imaginary. Okay, so there was a need for such things and These numbers came into existence Now most of you would be knowing that we have already started talking about Two-dimensional complex numbers which are called quaternions Okay, so when one of the English mathematician Hamilton, he has introduced quaternions into the system Lot of you know cryptographic work in the field of computer science has been done on quaternions and who knows 10 years down the line or 15 years down the line your children or grandchildren would be studying this as one of the chapters in Class 11th and 12th Jee may be famous questions on quaternions, right? So what I want to convey is the field of maths is dynamic, right? It is not like You know something which has been already decided and you have to work only with it There are a lot of debates a lot of changes are happening in the field of maths number theory Lot of research work is still happening. Okay Yeah, you read about that quaternions Sorry, I don't want to waste time talking about things which are not relevant as of now for our JEE preparation So this is a brief history why complex numbers came into picture. Now. What is complex numbers complex numbers are basically a bigger set which encompasses Real as well as imaginary numbers. Okay, so this is called a complex number We normally write it with a C with a slight stroke over it. Okay So real numbers are actually complex numbers Imaginary numbers also complex numbers and a combination of this is also a complex number So complex number is the broader set as of now. It is more broader than your real number set Okay So before I start going into more details about what's the complex number? Okay, and what kind of operations we can do it do on it. I would like just to give you a brief idea about The content of our study So overview of our chapter What are we going to study under this chapter? The first thing that we are going to study under this chapter is representation of complex numbers representation of complex numbers Okay There are three types of representation, which I'll be discussing with you point form polar form and Euler's form and We'll see how One form is helpful vis-a-vis the other in certain type of cases We'll be also talking about operations on complex numbers Operations on complex numbers. This is going to be the elephant in the room because It's going to take a lot of time because we have operations of addition Before that comparison addition subtraction multiplication division log Square root nth power They're raising one complex number to the other all those operations will be taken care So I think operation itself would be around two and a half hours of you know Subject matter for us under complex numbers Third we are going to talk about third. You are going to talk about the D Moavres theorem D Moavres this the pronunciation is D Moavre D Moavres theorem Okay, so the help of D Moavres theorem. We are going to talk about a lot of things Like finding the finding the n-th n-th power of Of our complex number Okay, and how this helps us in studying the n-th Roots of Unity in particular Okay, which also includes your cube root of unity including your cube root of unity including Cube root of unity roots of unity Okay Next thing that we're going to talk about is your rotation theorem a rotation theorem and This is something where we'll be introducing a new type of formula to you called the Kony's rotation formula Kony rotation formula Okay, this is a slightly tricky concept of all the four that we have discussed so far. It requires a bit of practice We'll do that through questions not to worry next we'll talk about Next we'll talk about the application of complex numbers application of complex numbers in Geometry numbers in geometry Okay, and when I say that I basically mean how it is used to find find Locusts or you can say solving Locusts questions Solving Locusts questions Locust problems Okay The last part that I have written for you This is a favorite of Jay Jay loves this like anything, okay? So they want you to understand all the operations that you are going to come across in complex numbers To the idea of Locusts Locusts is also a subject matter of coordinate geometry Right, so you would understand that how important Locusts becomes overall for you So this is I innocent in a nutshell. This is what we are going to cover in this chapter Looks to be simple only five concepts are there, but each of these concepts are pretty long, right? Representation of complex number itself is going to take us one one and a half hours today Okay, and some of the operations we are going to introduce today in today's class. So this is the overall Content of your complex number chapter Now how many classes will take for this? I Think three classes minimum It may go beyond I just some of you have asked me about the the share a break. Sorry, not the share a break Christmas break Christmas break. Yeah, so Christmas break is basically not there We are giving how we're off son 25th because that's the actual Christmas day so 25th if at all you have a class that will not happen and 31st and first Being the last in the first day of the year and the next year that will be off But the bad thing is or the good thing for most of you would be even those classes will be compensated somehow before the Actual holidays, so you may have to you know come on a non-centum day for a class. Okay, we'll put those dates In advance to you. Don't worry about it Mother. Yes, you did not miss a lot of things. We just started talking about the overview of the chapter So you can treat this to be the very first slide Okay All right So what is a complex number a complex number is actually a two-dimensional number? Okay, it is a two-dimensional number a plus B. I Okay, now here you are seeing something very you know interesting. I what is I? Okay, now I is basically The first word are the first letter of the word imaginary Okay, many people call it as iota also. Okay, it is under root of minus one Now what is this under root of minus one doing over here? Why do we need it? See as I already discussed with you Complex number is a two-dimensional number. It has got a real dimension to it and it has gotten imaginary dimension to it Let me explain this with the help of vectors. I'm sure you all have done 2d vectors in physics Correct. You have all done 2d vectors. Okay. Let's say I have a vector vector P Okay, if I write the vector P Or if my let's say vector P says that I'm just giving an example to you Let's say this vector P isn't such a direction that in order to reach from initial to the terminal position You have to go three units to the right and you have to go four units to the top Right, how do you signify such a vector? You will say sir. Beerah sir has taught us to write it as 3i cap plus 4j cap Correct. Yes or no, right Absolutely correct. I'm not denying it. Absolutely correct. Now why 3i cap and 4j cap? Why didn't you just write 3 plus 4? You'll say sir for two reasons. First of all, how would I know that this is a vector quantity? Second thing, how would I know how much I have to travel along x-axis and how much I have to travel along y-axis in order to You know go from the initial to the terminal position, right? So this i cap and j cap are basically unit vectors which tell you that Okay, you are going three unit Along the x-axis that means you are covering that i unit three times And you are covering this j unit four times in order to you know cover the entire vector, isn't it? In the same way when you write any real number, let's say you write a real number five You know actually you write five into one Because five means this unit one has been written five times So this unit is very important when you are signifying any type of real quantity around you or any kind of a physical quantity around you five mangoes If I just say five, how will you come to know which quantity I'm talking about? So one mango is like a unit and that unit is five times and hence, you know, okay He's talking about five mangoes. That's almost you know, two kgs of mangoes if you talk about the bigger ones, right? So unit plays a very important role Right. So when we write any number There is a hidden unit called one there when I'm talking about real numbers In the same way the unit for imaginary numbers is I So if I just write a plus B and let's say A and B are real quantities You will not be able to understand what is the real part of it and what is the imaginary part of it? Just like in this vector if I just write three plus four You will not know how much I component I have covered how much the component I've covered So when I say a plus bi I actually mean a into one plus B into I So basically I acts like a unit For signifying how much imaginary character that complex number has Are you getting my one acts like a unit to show how much real character that complex number has so it has both the characters So I acts like you can say distinguisher Or you can say a separator through which you can understand that okay This complex number has B amount of imaginary character to it Are you getting my point? Okay, so hence this I was chosen and since they wanted to it to resonate very closely with one unity That's why they chose negative one under root because this could be this could act like a very safe unit or signifying complex numbers Now many people may ask me sir. Can you write it like a comma B also because no people can understand that okay the first Element of the ordered pair is your real part second element of the ordered pairs of imaginary part Yes, we definitely follow this in practice right we also write complex number like a point Okay, that is something which I'll talk about in some time but is it clear that when you represent a complex number as a plus I be a Into one will behave as the real B into I is the imaginary of That complex number However, one thing I would like to emphasize over here that both a and B Even though a is called the real part of the complex number. I should not write belongs to I should say equal to and B is called the imaginary part of the complex number Even though this is what we name it but in reality a and B are real numbers only Yes, a and B are real numbers only I have seen people making a lot of mistakes while you know explaining it when I say Tell me the imaginary part of this complex number Watch out listen my question carefully. What is the imaginary part of this complex number many people say bi? No Imaginary part of the complex number is just be What is the real part of the complex number a? Are you getting my point? For example, if I say what is the j component of this vector? You'll say for don't say for j What is the real part a what is the imaginary part B? Now along with I it becomes an imaginary number For example here for along with j becomes the the j component. I mean you can say the j You know the component of the vector along the j direction Okay, so here, please be very careful when you are using the word Now that kvpy has done away with the interview But if that's a if you're appearing for a kvpy interview such wrong choice of words will give you a negative in your points Is this fine? So a is the real part B is the imaginary part both a and b are actually real numbers As you can see let's say I take an example of 2 plus 3 I Okay, 2 and 3 both are real numbers 2 and 3 both are real numbers, but we'll say real part is 2 imaginary part is 3 imaginary part is 3 Okay, don't use 3 I 3 is the imaginary part. Okay, so please be careful about the use of your terms Is this fine? now this I Will talk about it a little bit more because we are going to speak We are going to speak not only I as a Separator, but also I as a complex number or you can say imaginary number in itself So we'll talk about I so we'll talk about Properties of I the first property That you would observe is that It is such a number which when squared will give you a negative answer Okay, so I value is under root of Minus one so if you square it you will get a negative one right so Let's not be surprised anymore because now we'll be going now We are going to see such kind of activities quite a lot that square of a number can give me a negative answer Okay second thing is if you see If I just raise some powers to I let's say Okay, just keep watching these powers Okay, you would realize that it is following a cyclic nature That means after every change of four in the power it is repeating its previous value You see this Okay, as you can see I to the power one I to the power five I to the power nine They're all II each Okay, so after every change in the power of four it is regaining its previous value Okay, I to the power to I to the power six I to the part and I to the power 14 and so on and so forth they will all be minus one Okay, so this is following a cyclic kind of a nature. So this is following a cyclic kind of a nature Okay, third thing that you would observe from here is that if you raise I to any power which is a multiple of four and Being some integer you will always get a one check out this one I to the power four I to the power eight I to the part 12 I to the power 16. Okay, so if somebody asks you hey, how much is I to the power four thousand and four Without much waste of time you can easily say it's one because this is a multiple of four So I raised to any multiple of four will give you one Along with it you can also observe that I to the power four n plus one is going to be I I to the power four n plus two is going to be minus one and I to the power four n plus three is going to be Minus I Okay, so please make a note of this So if I is raised to any power which is leaving a remainder of one when divided by four That will give you an I eventually I Race to the power any number or any integer which is leaving a remainder of two when divided by four will give you a minus one eventually and I raised to the power any integral power which leaves a remainder of three when divided by four will give you a minus Fourth property that you should note down if you if you add any four consecutive powers of I If you add any four consecutive powers of I it is going to give you a zero I to the power zero is one Because it comes under this category. No zero is a multiple of four mother. So I to the power zero will be one Okay, so this is very important. Please note down any four consecutive powers of I any four consecutive or consecutive You know powers you can say integral powers also, but it can work for any any case power of I Will always add up to give you a zero What are the proof for this proof is very simple? Taken I to the power n common It'll give you one plus I plus I square plus IQ Okay, and I square we know is minus one IQ we know is minus I So one minus one cancels I minus I cancels giving you a zero Okay, so these are the four important properties that we need to keep in our mind While solving questions based on I Okay, any any doubt so far any doubt so far in whatever we have done. Okay. Let's take questions Let's take questions Sorry, I think this is complex them vector question go back to the desktop complex numbers So many questions that I need to start with the relevant question. Okay, I think it's sad so many Okay, let's do these simple questions Let me start with the first one Evaluate this that means I write it in a simpler form Evaluate this Or let me give you this question if you have to write this as a plus bi what will be a and b What will be a and b? Let's start with the first one Five or more consecutive term It'll depend upon which is your fifth term because till four it will be zero. No first one done Very good. Okay. So first one was I Plus I square now I square is minus one I to the power of four is one In the denominator, you'll have one again a minus one and This will be again a plus one. So this will leave you with an eye.  Let's do the third one third one is quite easy Okay, actually one more thing I would like to highlight away when you say negative six under root It is basically written as root six I It is written as root six I Okay, so when you're doing negative of Negative six it is basically negative root six I now go ahead and solve this question You have to write it in a simpler form Okay, but now very good. So let's cube it if you cube it you get minus six root six I cube Remember I cube is minus I so it'll be six root six I So you can write it as zero plus six root six I so a is going to be zero and B is going to be six root six Provided I want to write it as a plus B. I Okay Next one We'll do the third one. I think fourth one we can take it for the later or we can do fourth one also no issues Yeah, third one. What's the answer? Express this as a plus B. I form Express this as a plus B. I form Now, please put the question number so that I know you are answering for which of the above questions Okay, very good. Aditya Pranav shares Very good Okay, now you have summation I to the power P from P equal to zero to 300 So when you're writing it You write a Pete I to the power zero I to the power one I to the power two I to the power three I to the power four Let's put this in brackets. I to the power five I to the power six I to the power seven I to the power eight Let's put this in brackets And I'm sure you must be realizing why I'm putting those in packets Okay, so the last few numbers would be 300 I think 298 is uh No, uh 96 300 is also multiple so I can have I to the power 300 I to the power two 99 I to the power two 98 I to the power two 97 Okay Now if you see the reason why I have put them into brackets is because Four consecutive will add up to zero So this will be zero. This will be zero and all these numbers that you'll get will be zero each Which property have I used? Which property have I used over here? The fact that some of four consecutive powers of five will add up to give you zero Ultimately your answer will be I to the power zero, which is one Okay, so you can write it as one plus zero I One plus zero I Is this fine? Okay Let's do the fourth one Let's do the fourth one one plus I By one minus I square. Okay. Now before we square it Let's try to write it in a simpler form Now, uh, we have not officially done the concept of conjugate of a complex number But whenever somebody sees a problem like this The natural feeling that he or she will get is let's multiply it with This okay the same feeling of rationalization will come in your mind Correct Okay, so let's do this So when you uh multiply one minus I with one plus I you'll get one minus I square Okay, and on the numerator you'll have one plus I to the power of two Now what I wanted to discuss with you here is that Normally when you have such kind of powers or such kind of you know terms coming up We use our normal identity that we have learned a plus b the whole square. There's no difference between uh, you know Applying those identities to real number and applying those identities to a Non-real number or imaginary number the identities won't change. Don't don't worry about that So when you write one plus I the whole square you can write it as one square I square plus two into one into I the normal formula a plus b the whole square formula And in the denominator you have one minus of minus one Okay, now let us write down the values One square is one I square is minus one This is two I divided by two one plus one is two I minus I cancels two and two cancels so that will give you an I So the very first term that you have over here. This is actually I square. This is actually I square okay, so Without wasting much time Without wasting much time if this is I square The other term has to be reciprocal of I square correct So if this is I square Then this is one by I square Because it is just exactly reciprocal of this term So I square is minus one I square Again is a minus one. So this will give you a minus two Is this fine Any problem in this Okay, one interesting thing which I forgot to discuss with you How would he get the same answer if you squared it at the start If you squared it at the start Oh, you can do that no difference Multiple ways to solve the question mother So you may decide you may start you may square the numerator. You may square the denominator. Yes That is also going to give you the same result No difference no difference at all Now one very interesting fact When very interesting fact in fact, it's a myth. It's a it's a wrong notion that I would like to you to you know understand When we say under root of a into under root of b Okay, many people construe this as under root of ab Okay, please note that this formula works if at least If at least One of a and b is greater than equal to zero That means if both of them are negative this formula will fail Okay, how this formula will fail? So let me show you that So let's say I take a as negative four B as negative nine Okay under root of a would be under root of negative four, which is actually two i Under root of b under root of b will be under root of negative nine, which is three i Okay, so when you multiply them You will get two i into three i which is six i square Six i square is minus six Okay, now if you claim that this is equal to under root of ab Under root of ab in this case would give you a six Okay, and these two things are not equal That means this formula will not work under those circumstances So here is something very important for you to note down Under root of a into under root of b would become negative under root mod a mod b If your a and b both are negatives If your a and b both are negatives Okay, please make a note of this So people who blindly use this formula for everything Here is a word of caution. Here's a word of warning. Do not use this if a and b both are negative quantities Here a and b both are negative quantities. So the formula will slightly change Now why does the formula slightly change because this convention has been derived from the concept of geometric mean Which will study in the chapter sequence series and progression Now the moment somebody hears the word mean Or the word mean itself was coined to show something in between So whether you talk about arithmetic mean geometric mean harmonic mean It basically is a quantity which is between two numbers Right, so if somebody says What is the geometric mean of minus four and minus nine? So basically, I mean some of you would be already knowing it geometric mean is under root of ab, correct So under root of ab just like arithmetic mean is a plus b by two Geometric mean is defined as under root of ab Under root of full ab product Now we haven't done that chapter yet. So most of you would not be aware of it But those who are aware they would know that it is written as under root ab So under root of ab should give you an answer which is between minus four and minus nine When I say between not exactly midway, but somewhere between it. So it must be a negative quantity, right? So how can My answer becomes six. So this cannot be accepted as our right answer So it should be somewhere in between minus four and minus nine And hence this change in the formula has happened because of that Okay, these are just conventions which are made by you know, uh, no mathematicians to make To give uniformity across the field of mathematics Okay, so very interesting fact note down I've seen even teachers making this mistake Okay, so one question I would like to take up with you Let's pull out one from our I'll put the poll on. I'm not taking the attendance so if at all You have left the call now. You only marked as absent shake So the question as you can see on your screen is a sequence which goes from i To i square three i cube all the way till hundred terms And this expression simplifies to which of the following Two of you have answered so far good nice Last 30 seconds Last 30 seconds and I'll close this all right five four three two one Cool. All right 50 of those who have voted have said option number a Okay Next highest vote has gone to c. Let's check See, uh, this is a special type of series which you will learn sooner or later in the chapter sequence series and progression Which is called an agp agp agp. It stands for arithmetic o geometric progression Uh, there is a particular way to solve these kind of questions Which i'm doubtful that most of you would be knowing So let me take this as an opportunity to tell you that So if I write till hundred terms for this It will be this right Now in an agp like this first of all why the name agp was given because as you can see This kind of a series exhibits two types of uh progression characteristics One is an arithmetic progression as you can see the number one two three four Da-da-da-da-da-da-da So this is showing you an arithmetic progression characteristic And the second type is like it shows you the geometric progression characteristics i i square i cube i to the power four Da-da-da-da-da till i to the power hundred. Okay So when a progression, sorry when a series shows both types of uh, you can say characteristic We call those as an ag Arithmetic geometric series. Okay Arithmetic geometric progression if you don't write a plus in between So how do we uh solve such kind of uh series? What do we do is we first see what is the common ratio of the gp involved over here As you can all see the common ratio of the gp involved here is i isn't it Don't worry about the ap involved. Just worry about the gp involved So the gp involved has a common ratio i correct So multiply s with i So when you're multiplying it Write it one shifted to the right. For example, if you multiply this with an i right underneath this If you multiply second term with an i right underneath this If you multiply third term with an i right underneath this Okay, and so on so Ultimately, this will have 99 i to the power hundred and it will Just shoot this particular last figure and become 100 i to the power hundred and one 100 correct Let's subtract Let's subtract So s minus is will be like s one minus i take s common Uh, consider a zero over here if nothing is written and consider a zero over here if nothing is written So i minus zero will be i Two i square minus i square will be i square This will be i cube. This will be i to the power four and so on This will be again i to the power hundred And this will be sorry minus hundred i to the power hundred and one Okay, now here if you see there will be 25 such you can say No four terms I'll just show you one more So if you start grouping it, there'll be 25 such groups like this that will be created along with hundred Okay, so So they will all be zero zero each isn't it? Because we have all seen that We have all seen that Four consecutive powers of i will add up to give you zero correct So i one i two i three i four zero i five i six i seven i eight zero i nine i ten i eleven i two zero like that So if you go to i let's say 97 98 99 100 They'll add up to give you zero. Okay, so nothing is left other than Other than minus hundred one minus i on the right side Oh, sorry my mind hundred i to the power hundred and one sorry and that also is hundred i to the power hundred and one is like i to the power hundred Into i to the power one so i to the power hundred will become a one Because hundred is a multiple of four correct So ultimately what you see is Minus hundred i on the right side Okay, so our answer here would be Minus hundred i divided by one minus i If you look at the options None of the options so far resemble it So what i'm going to do is i'm going to slightly simplify this by multiplying with one one plus i So on the numerator i will get this on the denominator i'll get a one minus i square which is two So two and hundred will get cancelled 50 And if you multiply i inside will give you i square which is minus one And plus i So this will give you 50 times one minus i which i think is Option number So janta was absolutely correct. A is the right option for this Is that clear any questions any concerns? All right, let's take one more question Anybody has any question with respect to this Sir in the previous page What would have happened if one of the numbers were negative? Okay, you're asking me the previous page doubt One of the numbers were negative only one of the numbers were negative, right? If only one where negative other is positive or zero you'll follow the first formula If both are negative both the formulas Are you getting my point? Is that your question mother? Or are you talking about geometric mean when one is positive one is negative? geometric mean When one is positive another is negative is not defined because both are real numbers and your answer will come out to be imaginary That i will talk when i do geometric mean with you Sir, i just checked the first four terms pattern. Can we do it? For any sir sequence. Yes. Are you talking about the approach that we followed? The approach that we followed multiplying with the common ratio and subtracting it. Yes, that is a Widely followed approach. It can solve any a g s problem a g s means arithmetical geometric series problem by the use of that approach Yes, if one of them is negative other is positive you can use under root a under root b is equal to under root a b No problem with that For example, if you do under root of four into under root of nine Okay, it is same as under root of four into nine. So this will give you two y This will give you three this will give you under root of 36 Which is equal to six i and this is also equal to six i both are correct So it is matching with our formula Got it mother. Is this what you want us wanted me to explain? all right, so next question that I have for you is if x is equal to minus five plus two root minus four simplify Simplify x to the power four nine x cube Plus 35 x square minus x plus four Simplify means write it in a simpler format Or you get or I can say write it as some a plus i b Okay, uh, how many of you are actually solving this question? Uh, by the way, this is four i if I'm not mistaken Yeah, root root of negative four is four two i two into two, uh, four i How many if you're actually literally putting x value in all these places and trying to simplify I'm sure most of you are doing that. Isn't it? Now, let me cut you short on that if you are trying to do that because it is going to take a lot of time Right, you are not dealing with simpler powers raising it to a power of four cube, etc. That is going to take away considerable amount of your time Okay, so here is an approach that I would like you to understand Let us try to play with this expression So let's take the minus five to the other side Let's square both the sides So if you square both the sides, this is what you end up seeing Oh, it was four i my bad So you'll end up seeing something like this x square plus 10 x plus 41 equal to zero correct now All of you please pay attention. I'm going to tell you a very interesting and shortcut way This term you treat it as a dividend and this term you treat it as a divisor So this is your divisor. This is your Dividend and divide it by using your long division method By using your long division method I'll tell you why am I doing this just be with me for Few seconds So when you divide you get x square, this is x to the power of four 10 x cube 41 x square When you subtract you get minus x cube Minus six x square so put a minus x Again, when you subtract you get four x square. Let me copy this You get 40 x Plus four Just put a four So four x square plus 40 x plus 164 And subtract it We'll end up getting minus 160 as your remainder, right? So what I'm trying to say here is This term which you were actually trying to figure out. What is this expression? It could be written in an alternative way as This Into this right By Euclid's division algorithm. I can write this expression as quotient Times divisor plus remainder Right now you must be wondering why at all I'm doing this is because when you're putting x as five Sorry minus five plus four i here. That means you're putting x as minus five plus four i here also But this guy this guy is zero when you're putting x as minus five plus four i because this came from This fact if this is zero that means zero into something whatever it is It will be zero and you'll be left with minus 160 only So your answer will be minus 160 Right, so you don't have to put a minus five plus four i in every x and try to simplify that that is going to take at least five minutes of your time easily But this was just a case of a long division method which will take one minute or so and then you are done with your answer First of all the word remember itself is A misnomer never remember anything This method is basically if you incorporate it while solving questions, that is what I can say is the right use of word See whether what I did was I'm actually finding out the expression of this polynomial when you're putting x as minus five plus four i correct So this term I wrote it like this and finally I realized that When you put minus five plus four i into this you will end up getting a zero as the answer correct So what I did was I wrote my dividend which is your this term As this times quotient plus the remainder Okay, why did I do like that is because I know that this guy is going to give me a zero So whatever is the you know quotient I don't care everything will become a zero and whatever is the remainder Actually in that I have to put my value of x and get the answer. But since there was no x here Let us say hypothetically speaking. Let's say if there was some x term remaining Then you only have to evaluate that remainder part You don't have to worry about the other terms because they are anyways getting multiplied to This term which is zero And hence everything will become zero there. So remainder only will give you the desired answer Getting it whatever what I'm trying to say Make sense Okay all right So with this we close the i chapter of course we have done a lot of properties of i and We are ready to talk about now the next part of the chapter


Now this evening we're going to be talking about something I was actually saying to my guest that it's one of those things that I need, one of my properties actually has an issue in this particular department and I know so many of us, you know, want a solution to this because it also has a way of creeping up on you financially if it is not adequately addressed. We are looking at smart water solutions and how they affect property. We don't even look at what we mean by smart water solutions and of course what are some of the ways that you can go about to make sure that you're as efficient when it comes to all things water solutions in your property and help us get a better understanding of how we can be more efficient and certainly do a better job of this. I'm joined by Richard Feon who is CEO and founder at Power Optimal. Richard good evening and thank you so much for joining us on the show. Very good evening to you ma'am and thank you for hosting me and I hope that I can provide some useful insights for the audience this evening. I'm looking forward to our conversation Richard. I know one of the big things with our conversation I want to actually start with when we talk about smart water solutions what exactly are we talking about? Well we're talking about solutions that span the entire value chain of hot water and I think if I'd like to take a couple of steps back and talk about what motivated us to become involved in this particular sector together with our partner Electrolux and the primary motivation that started us on this smart hot water journey was environmental and the vision that we share with Electrolux globally is to be able to build a business that measures and manages a reduced carbon footprint generated from hot water and with that is the starting point and alongside Electrolux and their global aspirations for the environment and for their customers we've brought about a situation where we have a smart hot water system and a smart hot water system but definition is something that allows us to measure manage and reward so to say people that are involved in the utilization of hot water so that may or may not be an adequate description but let's take it from this angle if we look at hot water the energy cost to generate hot water is about 40 to 50 percent of the total household cost of energy and a smart hot water system allows us to reduce that consistently and significantly I hope that's a good definition for the audience and it certainly is I think when we like that you even point out Richard the cost of you know high water oftentimes whenever we speak to you know certain experts that we have on the show they'll tell us how how expensive our Giza usage typically tends to be I think it accounts for about 40 percent of your electrical bill comes from the Giza and so if you're able to find alternative ways of you know whether it's a Giza or even another you know device because we do know that there are other things that you can use instead of we'll say the classical Giza that gets connected to your electrical you know connection that still is able to provide you with water so the moment you have something like that you do find that people's electricity bill does actually significantly you know look different or lower than those of us who are still fully using our Giza and sometimes don't even switch it off I mean I know I can be very bad with you know switching it off manually and we have seen different innovations where there's the Giza trip that actually you know switches it on and off so that you don't have to remember because I know I tend to forget you know sometimes as as much as I want to before leaving the house switch it off or then switch it on when I come back it slips my mind and and I think I sometimes wonder you know what my electrical bill will look like if it was a way to to just be on top of that and I'm sure that's you know certainly something that people at home would want to get the better insight on I think you wanted to come in the Richard yes you know you say switching your Giza on and off to save money there is absolutely no benefit to doing that whatsoever when we do the physics and the calculations if you want to save money the first thing to do with any Giza a standard Giza a non-smart you know Giza is to throw a Giza blanket over it and that will give you some significant savings more savings than a human trying to manage it because we think we understand how these things work but sadly we don't and of course you know one of the key features of of the offering that we're bringing to the market the Elon smart water offering is solar connectivity can that's the ability to connect the smart Giza and you know the smart section of things to solar panels and solar PV panels generate electricity and if we generate electricity using the sun well we have a fixed cost to start to do that and beyond that we have very very small costs and we can do this at scale and we can do it it's become more and more cost effective over the years when we started our journey here the cost of solar panels and the cost of the energy that they deliver it was between seven and eight times what it is today and the cost of solar PV continues to fall at a very very high rate and the performance goes up it's a little bit like the personal computer when I first joined Apple in the mid eighties it cost you two years pay to buy a computer and you know now of course computers are well nowhere near in in many instances if we look at you know a certain part of society one month's pay and the other thing that I think is very important to consider here is we need to make energy accessible to all people and solar PV as a technology setting aside hot water for a moment is the vehicle that will do that the solar PV revolution has not yet started and you know one of the wonderful things is as as the adoption grows as happened with computers the costs will drop they'll fall and the difference of course with solar PV is that it will create lots and lots of jobs in Africa it will be one of the biggest job engines that we have so you know the inclusive transition to energy can also include and very much will include you know solar PV as part of that equation and the cost of solar PV generation or production when you buy it is a fixed cost and we and that fixes a particular cost per kilowatt hour and from there we all understand you know that escom will continue to increase prices year on year under normal conditions and under the current conditions we find escom in it's going to be way ahead of inflation so the payback just becomes really really really really worthwhile you know I often ask people the question why would you why would you hesitate to invest in being your own power station you know from a hot water point of view and when I put the argument to them they'll buy a car and lose lots of money and depreciation and get no return on it and and the residents to spend you know 20 20 odd thousand rand you know which is the cost of a full system to get a return on it of about 400 rand a month from day one they actually don't have an answer to that question and there are I think with the way things are developing in South Africa I think we're going to see the banks come forward and play a much larger role in making the funding available to make these things affordable in fact if we look at the saving that an average three bedroom house achieves by using solar energy to to heat its hot water in a managed fashion it's between four and five hundred rand a month and that pays for the system so we've reached that tipping point where I think consumers are starting to be very very aware of the fact that there's savings to be made and you know for a very small investment that can happen if you are just joining us this evening I'm in conversation with Richard Fearon who's a CEO and founder at Power Optima we're looking at smart water solutions and how they affect property you know Richard I of course at home taking your questions and comments do tag your friends and family in this conversation I also just want to find out from your home some of the water issues that you may have based in your respective properties and homes and how you went about facing them sometimes I mean sometimes even when there's a water leakage in your property it's not always easy to spot it and you know you could easily rig up a water bill that goes into the thousands of rands because you weren't able to spot what was happening I mean this actually once happened in one of the properties where there was a leak you were not aware of it and you know a water bill that would have typically been less than a thousand rands per month ended up going to over you know 15 thousand rands for that particular month because water was just continuously coming out and nobody was aware that that is happening so that's certainly something that we know we want to always be on top of I can see more of you checking in pulling across saying voting for solar installation to be affordable sandy stimage checking in there on our facebook page also saw that we had somebody new at check my fishing line also checking in tagging their friends we've got Bianca combs also checking in Shaqon Shaqon checking in on our facebook page of course do you keep the love coming send those green hearts and also share your water saving tips and if you've already started using certain smart water solutions or because I think many of us have certainly done that for for electricity or see the value but sometimes don't think about it when it also comes to smart water solutions and the importance of also doing that now Roger I actually want us to look at some of these structural and even foundational issues from water damage that we could find out when I was saying to you that this is one of those topics that I've had different kinds of water issues in different properties and so finding the various ways to even identify a potential water issue and a way to not only solve it but mitigate for it you know potentially happening in the future is something that is so important for me because I think you sometimes don't realize what is missing in your overall system in the house until you're faced with that particular crisis and have to deal with the after effects so what what what can be some of the damage that we could potentially see especially structural even foundational when it comes to it being damaged by water I think let's start it let's start again at the Giza end of things and you know the Giza is an appliance it's basically an appliance with which we don't have any relationship it sits in our roof it's up there and as long as it works it's fine and the only time we know that it really exists is when it either is cold or it leaks and it causes damage to our property and not just our our ceilings and our carpets you know it can it can go a lot further than that the Elon smart water platform is an IoT an internet of things platform behind the scenes and what this does is it allows us to look on a tank by tank basis you know a Giza by Giza basis on up to many millions of units and we can start we can see leaks before they become major leaks and that is a very very important aspect for everyone involved for the banks for the insurance companies for the consumers you know there's a massive amount of of damage that occurs from hot water leakage and hot water systems that rupture and and things that go wrong in the roof so managing that and managing that proactively and having pre alerts for that is a very very important feature that we enable in the Elon smart water system and that in itself if we look at insurance premiums that we pay on on householders cover between 50 and 70 percent of the householders premium is allocated to Giza related incidents and consequential losses and you know whether you're a tenant whether you're a landlord an earner property investor you know you don't want those things to go wrong and one of the things that we are able to now do with the system is to allow that to be pre alerted so the the customer will actually be told there's something wrong it'll go to their mobile phone it will also if there's a service provider involved alert the service provider so risk mitigation and and and total prevention of damage to property from hot water related you know unanticipated incidents is a very very tight point of focus for the solution that we deliver and that is Richard Feon who is the CEO and founder at Power Optimal wrapping up the Wednesday edition of the private property podcast with myself Osamantouma Kumalo well that's it from the team and I this evening we'll be back on your screens tomorrow evening at 7 p.m. until then hoping you're staying home and staying safe


Item Number – SCP-158 Object Class – Euclid Special Containment Procedures – SCP-158 is installed in Operating Theater 7 in Bio-Research Area 12. Personnel are not to be allowed in, nor is power to be supplied to the room, unless they have submitted and had approved a proper clearance requisition formed to the Chief of Research. Professor R- Personnel wishing to use the device must request and read the entire transcribed instruction manual in full. During the device's use, two armed guards are to remain on standby outside the room at all times. In the event of an accident, all power must be cut to the room instantly, and guards are to examine the room carefully for any signs of misconduct. Misconduct will be punished in a manner decided by the Chief of Research on a case by case basis. Description – SCP-158 is a large mechanical arm, similar to one that one might find in an automotive factory, although the end attachment is unusually shaped, resembling a pointed tridactyl claw. Its optimal placement is to be installed and suspended upside down, its base attached to the ceiling in a room that has been built to accommodate. A series of cables are protruding from the base, and some are connected to a complex mobile console, complete with VDU, visual display unit, and full keyboard. The others should be connected to a working power supply if the device is to be operated successfully. At the bottom of the console, there is a dispensing device with attachments for a container roughly 7.6 cm, or 3 inches in width, and 17.8 cm, or 7 inches in height. The arm, cables, and console have sustained fire damage, though this is purely cosmetic and does not affect the device's performance. When activated, the device will take 20 minutes to boot up and become fully functional. When used correctly upon a living organism that displays cognition, SCP-158 will remove an unknown substance and transfer it through the dispensing device beneath the console. The optimum container for this substance is a glass jar or beaker that fits the attachments. After this action is performed, the organism that it was performed on will cease all higher brain functions, with only the activity in the brainstem continuing. The subject will not respond to external stimuli and will not exhibit any movement beyond basic reflex actions. The substance removed is gaseous, though its overall appearance and properties differ from subject to subject. The substance is an indefinite source of kinetic, electrical, heat, and light energy. Although the rate and output, again, differ from subject to subject, the average is relatively low. The device was found in late 2007 in a burned out hospital that had been in apparent disuse for a large discernible period of time. Rough estimations would put it at over 5 years. Along with the device was a badly damaged owner's manual, which contained instructions on how to use the device. These instructions have since been transcribed and copied numerous times, with a single copy always present in the containment room. While the instructions clearly state how to maintain and use the device, the chapters chronicling who built it and what exactly it did were too badly damaged to read, requiring a process of trial and error to find it. The device is also capable of reversing the extraction, placing the same, or a different substance back into the subject. When this action is performed, the subject will regain all cognitive and higher brain functions, but the total results differ, depending on whether or not it was the original substance extracted from the patient that was replaced. Addendum 01 Dr. Ruck suggests experimentation with D-class personnel and electronic equipment to attempt to reproduce SCP-168, SCP-1875, SCP-2306, or similar phenomena. Pending Addendum 01A Inspired by the previous addendum, regulator Ruck has hit on the ingenious notion of using SCP-158 on a test subject. Then, exposing the body to SCP-217 until the virus runs its course, and finally, re-injecting the contents back into the transmogrified body. And Ruck are extremely excited about this proposal, and have arranged a meeting with all 12 of the Ruck to discuss the far-reaching benefits of such a technique. Experiment Log 158AA Experiment Log of Dr. Heinrich Dreisch, a medical researcher assigned to SCP-158 Date 2008 Experiment 1 The device worked perfectly. It seems the damage to its casing was merely cosmetic, but more interesting was the substance extracted from subject 001A. It's a dark brown in color, and is some strange cross between liquid and gaseous states. It should be analyzed in around an hour. Attempts to get the subject to show any sort of brain activity since has, as of yet, met with no progress. Still, no great loss there. Experiment 2 This time, the substance was a light blue, and it seems more...active than the previous one. I wonder if it had anything to do with the difference in age. Experiment 3 The test results came back, but they were inconclusive. They couldn't find anything. Literally. There were no signs that the substance even existed, apart from the steady emitting of light and heat. Anything else? Nothing. Again, this subject has produced another different sample, different in color, and in the energy output. This is quite odd. Experiment 6 There was a slight accident involving my assistant Lucy. I'm not sure how she managed it, but she knocked the sample from subject 006B onto her laptop. The strange thing was, it was out of power beforehand. Now, it's running, despite the fact both the plug and battery have been removed. However, there are some irregularities in its actions. Small glitches. Nothing serious. It makes me wonder. Experiment 11 This is the last one for the night. This sample is different, just like all the rest, but I've been noticing some semblance of a pattern to it. After a few more experiments tomorrow, I believe I'll be able to elaborate. None of the subjects extracted from today have come out of the vegetative state. There's physically nothing wrong with them. Nothing at all. I've had them screened for every possible medical anomaly. They're just not there. Students are on, but nobody's home. Still, despite this, I'm keeping them restrained and under guard. And Lucy's laptop, just in case. With the kind of things that go on around here, it's better to be safe than sorry. Experiment 24 I was right. There is a pattern to it. I'm almost certain the irregularities in the energy output are caused by the subject's age and vitality. As for the difference in colors, I think it may be down to the subject's disposition, but I'm not sure. I need to run a couple more tests and get the original files on the subjects. Lucy's laptop is still running, despite not actually having a proper power supply for two days. There's no trace of the substance, internal or external. There's not even a mark on the casing. The irregularities are strange too. If left idle on a word processor, text will write itself, but it's gibberish. Still, it's an experiment that warrants some investigation. Experiment 27 I've tried putting the substances obtained from the subjects into a variety of mechanical and electronic devices. The results are surprising. All of them have begun to work independently of an external power source. The ones of an electrical nature exhibited slight glitches of an intermittent nature. The mechanical items worked far more smoothly, although there was still the occasional oddity. The experimentation on the subjects continues. I think we'll stop when we go through around 50. Experiment 45 The substances implanted in the objects have proven to be able to be removed from them using the machine. When they were extracted, they were exactly the same as beforehand, pre-implantation. We could use these as a type of infinite energy, but we'd have to find a way past the constant discrepancies in behavior. I've left the original one in Lucy's computer, much to her chagrin. The glitches seem to be getting more frequent and more specific. Now, it opens the word processor itself and types coherent sentences. I've saved them to file for research purposes. The camera and microphone activate themselves and try and remain on regardless of attempts to turn them off. After a while of doing that, the word processor opened and typed out the words, quit it, you a**hole. I'm submitting it for a Turing test. Experiment 49 The laptop passed the test and has displayed characteristics similar to Subject 006B, the original donor, although Subject states that it has no memory of the time passed when it was interred in the laptop. This confirms my suspicions. Against all logic and scientific reason, SCP-158 is a device that extracts what most people would term a soul. This only opens up the possibilities for experimentation. This session, however, is over. Dr. Dreish is promoted to the head of studies regarding SCP-158. Further experimentation on SCP-158 and its products will continue. Experiment log 158 AG Experiment log of Professor K. P. Crowe regarding SCP-158 in use for the Olympia project. Pre-experiment note I've gathered up several D-Class personnel, having interviewed and evaluated them all, and picked those with personalities and characteristics that I like or would be useful. Some are male, others are female, as I believe a soul transcends the flesh it is interred in. But the purpose of this experiment is to test the extra capabilities of the device, which was spoken upon in the heavily damaged sections of the book. I've poured over them incessantly, trying to glean as much information as possible from it, but the instructions I managed to get were sketchy at best, and downright unhelpful at worst. But that will not deter me. I'm a researcher. Trial and error are my middle names. Experiment 1 I withdrew the first subject's soul. Try as I might. I was unable to do anything extra to it, but then again, there was such a small window of time for me to utilize it and try everything. But on the bright side, I managed to reverse the process. While that had been done before, no one has discovered the sequence needed to activate, operating on blind luck. This is the first thing I'll concentrate on. Experiment 5 I've done it. It wasn't that hard. Experiment 6 You know, I've noticed that there's a small period in the middle of the operation where the process pauses, as if it's waiting for further commands. I think that's when the further inputs can be made. I'll have to start checking. Experiment 7 I've been removing and re-implanting the same soul into the same test subject, mainly as a form of experimentation with the controls, but also as practice. Oddly enough, there doesn't seem to be any sort of side effects regarding the subject's health. One would think there would be, considering what I'm doing to her. Regardless, I've been probing around that pause with the controls, and I think I almost have it. Experiment 8 I made it begin the movements of something else entirely before it paused again and resumed its original course. I almost have it. Experiment 11 I got it. It completely stopped during the pause, and a completely new set of options appeared on the monitor, being things like split, merge, remove aspects, add aspects, and combine aspects. From this, I can only deduce that the device is capable of internally storing and modifying these souls for use on other subjects. This is exactly what I was looking for. Experiment 12 The aspects that the machine talks about are difficult to define properly. They're all notated by a single word each, often something obscure from various religious texts. I've had to pour over the holy books of at least four major religions, and six minor ones, just to understand what the hell the machine is trying to tell me. And even then, I'm still not entirely sure I understand. As far as I know it, most of these aspects are facets of the person's personality and their general basic behavior, as well as things like willpower, understanding, conscience, creativity, empathy, and drive. This may take some time to truly figure out. Experiment 37 This is taking much, much longer than I had originally anticipated. So far I've discovered that a device itself can store up to ten different souls, and their composite aspects, and modify them internally. Finding out exactly what each aspect corresponds with is difficult to say the least. I'm having to modify each subject slightly, then send them out for a complete psychological evaluation to try and discern what exactly I did. Then I have to repeat the process several more times just to make sure. This is tiring to say the least, but on the upside, at least I'm becoming more proficient at the device. Experiment 42 This is getting ridiculous. This has sucked up most of the time in my day, and I'm near falling asleep here. There has to be a different way to monitor and measure the changes in these people's souls. I'm going to try and get onto R&D and see if they can find some sort of way of reverse engineering some part of this device, something to make this run just that little bit smoother, something to help us understand it more. I know how to operate it, but I'm shooting in the dark here.  I know which keys make which sounds, but I can't play a song to save my life. I'll try again tomorrow. Maybe the mourn will bring with it new ideas. Date 01-12-2008 Experiment 57 I had thought I had grasped an idea of the limits of this device, but I was proven wrong. I had assumed the machine was at fault, being too complicated for its own good. Now, I realize my mistake. It's not the machine, it's the very nature of a human soul. There's no true way to express something like that in mere words, although this machine tries desperately to do that. That said, it will take me some time to be able to use this device competently enough to do what I'm hoping to do. I'll have to study the things I've seen and recorded to the very limit of my abilities. Date 02-12-2008 Experiment 80 I've left the device alone for the moment, electing to study my notes, then raise more questions interacting with the device. I've recorded over 400 different words in regard to the aspects, with an almost unlimited number of combinations capable therein. Seems apt, of course, considering the complexity of the human condition. But, should I master this device, the possibilities could be endless. But such a thing does not seem to be anywhere in sight. It may take months, even years, simply to grasp this device, let alone do what I've suggested. I plan to do it in days. Date 03-12-2008 Experiment 93 Still no real progress. At most, I've gotten a single soul that is a composite of all I've learned, but it's something that I can't quite describe. When interred into a host, it's highly interesting, but when I send it in for a psych test, the results basically go out the window. We can't get a valid result, which in and of itself is impossible. Experiment 95 I've been modifying this composite soul, which I'll dub subject to zero for the time being, and every time I do so, I get the feeling there's more to this than meets the eye. It seems to be more aware of its surroundings, more knowledgeable than its hosts should allow, displaying an intellect that would outstrip most researchers in this place many times over. Possibly even me. Experiment 107 My god, this is unprecedented. The reason why the evaluations were so inconclusive, why zero seems so knowledgeable, why it seemed to be able to see another world around it, they all make sense now. Subject zero by some fluke of chance, or by my meddling with this machine somehow, simultaneously exists on this plane of existence and several others. I have created an entity that exists beyond the scope of human interaction, a consciousness that can see and hear and feel and think outside of this realm. It is aware of what I've been doing, and it appreciates me having created it. It is, in a sense, immortal. Even if its physical host is destroyed, it is capable of continuing to survive beyond that, only slightly limited in this level of existence. It revealed the truth to me, and I've asked it to answer my questions for the evaluation honestly. It agreed. Experiment 110 Zero would make an excellent candidate for my assistant. It respects and admires me for its creation, much a child would an endearing father figure. I have assured it that it would be treated well, and that I will give it a host to the best of my ability to create. All that it asks of me is that it is given a name other than zero. A name, not a number. I told it to give itself a name, to christen itself whatever it so wishes. It told me it would have to think about it. End of session Notes. The composite soul has been accepted as a component for the Olympia project. Lesson complete. If you missed the previous orientation, go watch SCP-157, Mimetic Predator, right now. Or for the complete course, watch this playlist.