Hi, beautiful. What's going on? Today I'm gonna be showing you how to use the flat iron correctly to get the sexiest waves possible. That's right, I said it. Don't tell the other hot tools this, but I think the flat iron is my favorite. It's just so versatile. And who doesn't love a verse? Anything, really. This tool with two hot blades on it that go like that on top of each other can do so much and make your hair look incredible with very little effort. But I also know a lot of you girls are there and a lot of people with long hair don't know how to wave their hair. And I know this from first-hand experience because none of my girlfriends know how to do their hair well with a flat iron. It's sad and I wanna help the world. So I'll be showing you how to use the flat iron in three different ways in order to get three different kinds of waves. These things do take practice and a little bit of effort and a little bit of time to perfect, but I promise you, you can do it. It is not that difficult. Just pay attention today and take your time and be patient. And with that all said, let's get to waving, baby. Let's do some waves. My client has arrived. Thank you for coming. What? You're scared?  I have tortured some of your other siblings. Not all of them have gotten the best treatments, but you are lucky because all we're doing is ironing your hair today. So you're gonna be just fine. I promise, okay? We're not doing anything crazy today. We're not giving you a new color or a new haircut or experimenting with anything. So you'll be fine, all right? All right, good, okay. So in order to achieve today's looks, we're gonna need just a few things and really most of these are optional. We're gonna need a clip or multiple clips, a flat iron. You do not need the dicing corral, but I do love it. The cordless moment is everything. I'll also be using some force field heat shield to protect the hair from heat damage. And to finish everything off, I may use some salty sea salt spray. Those are the items for today. It's pretty simple. I am just going to be sectioning the hair into three different quadrants. That way I can show you guys three different techniques on three different sides of the head. So we're just gonna spray some force field heat shield over everything, just a light misting. And we're gonna brush that through. It smells so good. And I'm gonna put this at 365 degrees. You do not need super high temperatures for this. If you don't have extremely coarse, coily, kinky hair, you do not need like 410 degrees on your hair. Don't do that.  So we're gonna pick up a section that is about an inch and a half wide. Now watch closely. I'm gonna be doing one myself and then I'll show you guys how to do the other one. So I'm gonna pick up this small section and we're just gonna go for it. Wow. It's so pretty. I know that a lot of people can't do this one for some reason, but we're gonna do it again. I'm not gonna clamp it right now but I'm gonna show you what to do. So we're gonna clamp it down, turn halfway one way, pull, turn halfway the other way, pull, halfway the other way, pull, halfway the other way, pull. And the trick to making this look really nice and really put together is doing it slowly as well as evenly. If you pull down an inch this way, you have to pull down an inch the other way, okay?   So let me show you that again.  I'm sorry, but that looks delicious. Let's do it again. So make sure your sections are also not too thick and not too wide. This is how thick you want it. It's quite a thin section. This is going to give you even heat distribution and make sure the wave is all uniform and beautiful.   Wow, look how fun that is. Like, she looks gorge.  And when you're using the iron at a low temperature, you aren't gonna get as severe of a wave, which is good because I think when people do this too severely, like the wave is super crimped, I don't think it looks great.  Another great little tip with this is at the end, make sure you're always finishing with the end going in. And you can kind of cheat a little bit right at the end. You can quickly pull back before you finish the strand. That way the end goes inward and not outward because when they go outward, it just looks like really bad, trust me. This is also a great technique to do when you just woke up and your hair is kind of cute but like not perfectly cute and you just want a little bit of extra wave and extra something in there to make it really look finished and polished. This can do that. You don't have to do every single strand of your hair. You can just do kind of in between your natural waves and it'll add a really nice finished kind of look to the whole head. And that to me looks fabulous. And you can go on some of the pieces of hair and just refine it a little bit. If you don't like some pieces, just give it a little extra crimp and you'll be good to go. Let's add a little bit of salty sea salt spray to texturize this just a little bit. Ooh, that looks perfect. You can even put the salty in your hand and then just scrunch it in also. God, I love that. So that took me all of like three minutes to do. So easy. Seriously, if you just practice this a little bit, you will get the hang of it. Love that wave, probably my favorite but there's also some other cool waves you need to know about because I love combining different waves all into one head. I think it gives a really beautiful bohemian cool vibe when you combine different kinds of waves all in the same head.  Next wave, are you ready for this? Are you ready for this? I'm excited to show you what's about to go down. So let's spray keep protecting on nice and far away. You do not need to come up close and spray down the hair. This also acts as a little bit of a flexible hold on the hair so that your waves will stay all day, all night and all week if you really want them to. I want you to bear with me, okay? Because it can get a little complicated. I'm going to feed the hair in, make it into a little C and make a bunch of Cs. You get a really nice, beautiful flat wave. Some of you out there might be thinking, Brad, that looks hard but we're gonna simplify it. Please don't take too much hair by the way. This is a very fine thin section. Please do that. It's easier for you in the long run if you take smaller sections. You literally just hold it down, clamp the iron down and then drag the iron so it creates a C shape. See that? The next one, you're gonna just take it and just move it in the opposite direction and clamp the iron down. And then the next one, you're gonna start pulling it again. This wave also is super pretty because it's a little more natural looking than the rest. If you want that super lived and natural look, I think this is the best one to do. So let me show you again on another section. We're clamping, we're pulling. This is the only one that you're gonna be pulling like this. Okay? Then the rest, you literally just fish it in to the bottom of the iron and literally just form a wave with your fingers as it goes through the iron. You are creating this masterpiece by moving your fingers around and creating little C formations back and forth. Let me show you again because I know it all might be still confused. Clamp it down, pull. You're pulling, okay? You're pulling the hair into that first C and then the rest of them, you're just fishing little waves into the iron, okay? Exactly how you want them to lay. Clamp, pull. We got this, we got this girl. Come on. Fish those little C's in back and forth, left and right, left and right. All right, cool, cool, cool. Maybe make little shallower ones on the end. Beautiful. You can break it up with your fingers at the end.  Something about waving hair just makes me so happy. See that when you get good at it, you can do it in five seconds, all right? These things are going to take practice. They're not just gonna come in one second or maybe they will. You're creating the pattern and all the flat iron is doing is just adding the heat to keep it in place, okay? All right, let's finish off the rest. Okay, and so that is the finished wave without anything in it. Now, I'm gonna add a little bit of salt in there because I love the texture it gives me. I'm actually gonna put it on my hand. This is gonna add a little bit of texture, some more hydration. It has tons of oils in it. Just give it that sexy, lived-in hair look. I'm obsessed. I'm fully living. That's gonna dry really beautifully in the hair. So here we are. Let's compare the first one to the second wave. This looks even more natural. It's a lot flatter as well. This has really no volume to it whereas this one is definitely a little more three-dimensional and it's coming off the head and this one is laying super flat to the head. I mean, I love both. I think the volume this one gives me is amazing. The naturalness this one gives me is also just incredibly beautiful. And just like that, we have made it to the last and final wave. This one is definitely the most voluminous, the most refined looking one, but at the same time, a little disheveled looking and natural. You'll see in a second what I mean. It's a little bit of both. If you already know how to curl your hair with a flat iron, you're already leaps and bounds. What is that saying? I don't know. Leaps and bounds ahead of everybody else with this one. I don't know. Whatever. What we're gonna do is basically curl the hair halfway and let it go. You'll see. I'm gonna show you this first one. I'm not gonna explain it. And that is that. Do you see how much volume that one has? Oh, it looks hot. So this one is almost a curl, but it's still a wave. It's a combo of both of them. Now this is different than the first one because in the first one, we did it horizontally. We're doing it vertically this time. We're gonna turn the iron halfway, hold down a little bit and let it go. Right below that first wave, you're gonna do it again, but in the opposite direction. And then again after that in the opposite direction. You're gonna get this really defined, beautiful, almost curled S wave. Let go, turn, let go, turn, and let go. And feel free to go back in after you're done and kind of refine the waves the way you want them to look. That is totally okay. Now in this next section, I'm gonna show you the same technique, but done a little bit faster and a little bit differently.  You don't actually have to pull the iron out. That is a much easier way to do it when you first begin doing this kind of wave, but you can actually just do it all in one sweeping motion like this. So I'm actually just doing the same thing, but I'm not taking the iron off the hair at all. So we're just clamping it down, turning halfway, turning the other way halfway, turning the other way, turning the other way.  What I'm doing is just taking the iron and bending the hair a little bit more. We're getting amazing volume with this wave. If you have hair that is more on the finer side and it lacks volume, this is probably gonna be your go-to. Clamp it vertically, turn halfway, take it out if you want to, turn halfway, again, turn halfway. Oh, yes, baby. That is gorgeous. You look so pretty. Yay, yes. We're almost at the finish line here. These waves take no time at all.   And you see on that one, you can really see that it's giving you almost a curl, but it's not quite there yet. We're just gonna brush this top section and we're ready to finish off this side of the hair. Boom, clamp, boom, turn, boom, clamp, turn the other way. Boom, that's it. That's a little bit too curl at the ends for me. I don't like that, so I'm just gonna go, doop. That's it, just flatten it out a bit. All about using your eye and figuring out what you like and what you don't like, and then just correcting it. That's what makes a wave really look beautiful is when you just refine it a little bit at the end. And again, let's hit it with a little bit of salty on the hand. And this salt water is not super drying. I know there's a lot of formulas out there that are very drying and mine is definitely not. It's actually more on the moisturizing side of things. Even if you're spreading your hand and let it sit there, it's not gonna dry your hand out. And already, you can see just from this side, there's so much volume. This is like maxed volume. Look at the difference between the first side we did, which is a very similar method to this one, but look at the amount of volume we got there. We could have even added a little bit more lift at the top, but like that is gorgeous waves with a ton of texture and volume. When you look from the front, it almost looks curly, but on the side, you can tell it's waved rather than curled, and I love that. And if the ends are a little too stringy for you, you can totally brush through them a bit. I love this side. If you're looking for a max volume, max texture and maximum wave, this technique will really give it to you. Simply stunning and much different from everything else we did. So to wrap it up, these are the three different waves we did. This is what we started with. This beautiful flat defined wave. The second one, even more relaxed, almost straight, but with a little bit of texture, but still gorgeous. And definitely this one will be the flattest one of them all. So chic. And this last one is the most volumous of them all with even more curl to the wave. So once again, I love to combine more than one of these techniques on the same head. I honestly like to just feel it out, go for it, try different things. If you combine all these techniques on one head, it'll give it an even more lived in natural hair vibe. And people will literally think this is your natural wave pattern, which I think is so chic. Otherwise, honestly, pick one of these. They're all so pretty. So you're gonna live no matter what you choose. Those three wave patterns make me want long hair so I can play with it and look that chic. That's Manny Quinn, you did yourself today. You really rock that. So thank you. If you guys are not already subscribed, if you would like, you can do it right down below. You can also click the like button and the bell icon to be notified every time I post a new video. Thank you. Feel free to text me. This is my number. Yes, it's really connected to my phone. Yes, I really do see some of your messages. And yes, I'll be texting back a few of you guys. If you text me right now. If you guys are like, check out my hair care at my hair color brand, you can totally do that at xmodohair.com. You can find all of these colors that are in my hair right now on that website linked below. You can also check out some hair inspiration at xmodo hair for hair care and at xmodo color for color. You can follow me everywhere else here on my social media handles. Today's Instagram shout out goes to Tina and she says, hi Brad, I need your help with my hair. I'm a natural brunette and did blonde highlights but my highlights look yellow and I wanna go full blonde. What can I do? Okay, two things. You need to lighten your hair more. But honestly, if you have very dark, very coarse hair, your hair is probably always going to fall back to that yellow stage. So I recommend not pushing it too far. I actually really like this tone on you. I know you want that platinum blonde look but I like this better. It's more of a warmer blonde and I think it really compliments your skin. So I say stick with this and don't push your hair beyond its limit. Thank you guys so much for watching. Don't forget to live your extra life and I'll see you next time. Bye guys.


In this video we will consider some problems on Milne-Thompson method. Learning outcome at the end of this session students will be able to construct analytic function by using Milne-Thompson method. Pause this video and write down the answer for the question what is the formula for the derivative of an analytic function f of z. I hope all of you have written the answer. Now the answer is the derivative of any analytic function f of z is given as f dash of z is equal to ux plus i into vx and this derivative also has another form since f of z is an analytic therefore its real and imaginary part satisfies the CR equations ux equal to vy and uy equal to minus vx if we replace ux by vy and vx by minus uy we get the same derivative in the another form as f dash of z equal to vy minus i into uy. Let us consider one example find the analytic function f of z was imaginary part is e raised to x into x sin y plus y cos y solution here we have given the imaginary part therefore we will denote it by v step number one we are differentiating the given function v partially with respect to x and y so let us differentiate first v partially with respect to x treating y constant therefore we get vx equal to now here we can see that this is the product of two functions of x therefore we use the product rule to differentiate it that is first of all we will write e raised to x as it is and then differentiate the second function now here in the first term sin y is constant and the derivative of x is one plus in the second term x is not involved therefore its derivative is 0 plus write down the second term x into sin y plus y cos y as it is and the derivative of e raised to x is e raised to x after taking e raised to x common from these two terms we get e raised to x into sin y plus x sin y plus y cos y let us differentiate v partially with respect to y treating x constant we get v y equal to now the first term is of e raised to x which is constant let us write it as it is into inside the bracket while differentiating with respect to y x is constant and the derivative of sin y is cos y plus now in the second term we can see that this is what the product of two functions of y therefore in order to differentiate it we have to use the product rule writing y as it is derivative of cos y is minus sin y plus cos y as it is and the derivative of y is 1 now after simplifying it we get e raised to x into x cos y minus y sin y plus cos y step number two we know the formula for the derivative of an analytic function f of z that is f dash of z equal to u x plus i v x let us call it as equation number one now in the step number one we have obtained the expression for v x and v y and we can see that the derivative contains the term u x that is the partial derivative of u with respect to x which is not known to us now here now our aim is to replace this unknown function in terms of the known function in order to replace it in the step number three we are using cr equations the cr equations are given by u x equal to v y and u y equal to minus v x minus v x now here u x is v y replace in the equation number one u x by v y we get equation number one as f dash of z equal to v y plus i into v x the content involved in the right hand side is known to us let us replace v y and v x by its expression we get this function now to have the right hand side as a function of z let us put x equal to z and y equal to zero on the right hand side of equation two now we get f dash of z is equal to e raised to z into z cos zero minus zero into sin zero plus cos zero plus i into e raised to z inside the bracket sin zero plus z into sin zero plus zero into cos zero that is we get f dash of z equal to e raised to z as it is into we know that cos zero is one therefore z into one is z and here zero into sin zero is zero plus cos zero is one therefore it is plus one plus now here we can see that sin zero is zero again here sin zero it is also zero and zero into cos zero is zero it means this total bracket has the value zero therefore the second term is not written here now we have obtained the right hand side as a simple function of z let us integrate the above equation with respect to z to get f of z now integrating with respect to z we get integration of f dash of z is f of z is equal to integration of e raised to z into z plus one dz plus c integration constant now here we can see that this is the product of two functions of z therefore the generalized rule of integration is used to evaluate this integral we will consider z plus one as the first function and e raised to z as the second function now write down the first function as it is and the integration of e raised to z is e raised to z minus let us differentiate the first function z plus one with respect to z its derivative is one into one more time let us integrate e raised to z we get e raised to z plus c after simplifying it we get the final answer f of z as z into e raised to z plus c this is the required analytic function f of z let us consider one more example find the analytic function f of z was real part is sin 2x upon hyperbolic cos 2y minus cos 2x also find imaginary part solution as it is a real part we will denote it by u step number one let us differentiate u partially with respect to x now here we get here we can see that u is provided in terms of a rational function and the numerator as well as denominator contains x therefore to differentiate u partially with respect to x we have to use u by v rule now the rule is write denominator as it is and differentiate the numerator now the numerator is sin 2x its derivative is cos 2x into 2 minus write numerator sin 2x as it is into differentiating denominator with respect to x now it is a function of y therefore its derivative with respect to x is 0 minus now the derivative of cos 2x is minus sin 2x into 2 divided by denominator square now after simplification we get 2 hyperbolic cos 2y into cos 2x minus 2 cos square 2x minus 2 sin square 2x upon hyperbolic cos 2y minus cos 2x bracket square now in the second and third term we can see that it is possible to take minus 2 common and after taking minus 2 common the expression remained in the bracket is cos square 2x plus sin square 2x and its value is 1 therefore we get ux equal to 2 hyperbolic cos 2y into cos 2x minus 2 upon hyperbolic cos 2y minus cos 2x bracket square and similarly differentiating u partially with respect to y we get the derivative minus 2 sin 2x into hyperbolic sin 2y upon hyperbolic cos 2y minus cos 2x bracket square now let us use the formula for the derivative of f of z that is f dash of z equal to ux plus ivx let us call it as equation number one here vx is not known to us therefore let us use the cr equations the cr equations are ux equal to vy and uy equal to minus vx now here the second result is useful we can replace vx as minus uy therefore equation number one becomes f dash of z equal to ux minus i uy and we are knowing the expressions for ux and uy after substituting it we get this equation let us call it as equation number two now to get this right hand side as a function of z let us substitute x equal to z and y equal to zero on the right hand side of above equation two now we get f dash of z equal to two into if we put y zero it is hyperbolic cos of zero and hyperbolic cos of zero is one into cos of two z minus two divided by again this hyperbolic cos 2y is hyperbolic cos zero and its value is one minus cos of two z bracket square plus now here we can see that if I put y equal to zero here it is hyperbolic sin zero and its value zero therefore the imaginary part totally vanishes therefore we can write here plus i into zero now after taking minus two common from the first term in the numerator we get it as minus two into one minus cos of two z upon one minus cos two z bracket square let us remove one one minus cos two z from the numerator and denominator now we get f dash of z equal to minus two upon one minus cos of two z and again we know that one minus cos two z is nothing but two sin square z now we can remove this two and we get f dash of z as minus one upon sin square z and again we know that one upon sin is nothing but cos x therefore we can write minus one upon sin square z as minus cos x square z now the right hand side is obtained as a function of z integrating with respect to z we get now the integration of f dash is f of z is equal to minus is written outside the integral and the integration of cos x square z dz plus integration constant c and we know that integration of cos x square is minus cot z and this plus c as it is and finally we get it as cot z plus c now this is the required analytic function now to find the imaginary part from this analytic function we will write f of z as u plus iv and it is we have obtained as cot z and we know that cot z is nothing but cos z upon sin z again z is nothing but x plus i y therefore we get it as cos of x plus i y upon sin of x plus i y and it is equal to let us multiply and divide by sin of x minus i y now we will get this expression now we know the identity cos a into sin b is nothing but 1 by 2 sin of a plus b minus sin of a minus b now we will get this expression and in the denominator also we can use the identity that sin a into sin b that is equal to 1 by 2 cos of a minus b minus cos of a plus b now we will get this expression after applying this identity now this 1 by 2 will be removed and we get this numerator as sin 2 x minus sin 2 i y upon cos of 2 i y minus cos of 2 x that is equal to sin 2 x as it is and we know that sin 2 i y is nothing but i into hyperbolic sin of 2 y divided by and cos of 2 i y is nothing but hyperbolic cos of 2 y minus this cos 2 x as it is now if we separate it from the numerator we get u plus i v equal to sin 2 x upon hyperbolic cos 2 y minus cos 2 x plus i into minus hyperbolic sin 2 y upon hyperbolic cos 2 y minus cos 2 x now we can see that this is what the given real part in the problem and therefore definitely it is the required imaginary part therefore after comparing we get the imaginary part v as minus hyperbolic sin 2 y upon hyperbolic cos 2 y minus cos 2 x