Hi everyone, I'm part of the OpenContrail team and today I'll be talking about our Kubernetes and OpenShift integration for Contrail Networking. And towards the end, we also will be talking about AppFormix, so Travis will give you an overview about that. This is a general agenda for this topic today. Let me just give you a quick overview about Contrail. We are an SDN solution for OpenStack and currently we are also working on new container technologies such as Mesos, OpenShift and Kubernetes and providing an SDN solution for these containerization technologies. I'll also talk about a few things that we have done in terms of mapping Contrail resources to Kubernetes and the last thing is the new thing about Helm deployment that Contrail has used for both OpenStack and OpenContrail. To begin with, with the latest release, 4.0 Contrail, we have containerized our whole control plane, which means previously we were running all these processes on bare metal servers, but now all these are Docker containers as part of the new release. There are 4 containers, 3 controller containers, which means controller running, configuration and control node. There's an analytics container and an analytics DB container, which is our Cassandra database for storing all the stats and UVs. In addition, we have a Vrouter agent container, which runs on every compute node. So if you have a Kubernetes cluster with Kubernetes master will run the controller components and all the Kubernetes slave or minion nodes will run our Vrouter agent containers. In addition, we also have a kernel module, which is the Vrouter kernel module to handle our forwarding. Now, each of these containers, we have many ways to deploy, of course, Ansible, Puppet and so on, but the new thing that we are looking at for this release is Helm based deployment, which I'll show you a demo towards the end. Now, how does Contrail integrate? So what we've done is we've taken all our existing control plane and added some new components to interface with Kubernetes. Fundamentally, all the constructs that we always had in Contrail, we could leverage for any of the new container orchestrators, but some of the new components that we've added is to interface with Kubernetes components and it's the same in case of OpenShift as well. So in this case, what you see is a current Kubernetes deployment. You have the Kubernetes master running on top and then there are two minions of compute nodes in this case, which will handle scheduling of the pods. Now, Contrail comes in with a new component called ContrailCubeManager and the idea behind this is that it interfaces with Kubernetes API server. So everything in Kubernetes is backended by HCD and then you can watch the stream of events. So let's say a pod is getting scheduled on a particular compute node. Now that event, ContrailCubeManager is continuously watching that streaming API and based on that, it takes actions. Now the actions are allocating an IP address to that particular pod, finding out which compute node it's scheduled on, so creating the linkages for that pod to that particular compute node and so on. So the complete allocation of IP address is central and hence most of the job is done by ContrailCubeManager. There's another component that we have which is our CNI plugin. So we have open sourced a Golang based CNI binary for Contrail. So that's the container networking interface required to provide finally the IP address to the pod that is scheduled on a particular compute node. So if you notice at the bottom, the CNI plugin which is a Contrail CNI plugin will receive, will get invoked whenever the pod gets scheduled on that particular compute node. And that CNI plugin talks to our Contrail agent to retrieve the IP address that was centrally allocated. So it does that one thing and returns that to the cubelet component. In addition, it also plugs the vEath interface for the pod into the vRouter. And once that interface is plugged into the vRouter, all the forwarding that we have today in Contrail with our encapsulation and so on, we can leverage everything in terms of the basic forwarding paths. In addition, you can also leverage Contrail for all the additional features that we have in terms of network policy and so on. Now the first thing we had to figure out when, I mean that is a workflow that I just showed you but in terms of resource mapping, what you see on the left is what are all the resources that exist in Kubernetes. An important thing to see here is that there's no notion of a network resource in Kubernetes. So fundamentally, Kubernetes, when you deploy a cluster, it has three IP ranges, one IP range for allocating to pods, one IP range to allocate to services, and finally the last IP range if you need public access. So what we've had to do is figure out different mechanisms how we can create networks underneath a Kubernetes cluster. But before I jump into that, let's look at the current mapping of all the resources. Namespace is a notion of a virtual cluster in a Kubernetes cluster which we mapped to, you know, you could think of it as a Keystone project. It could be shared for all namespaces or each namespace can get its own project depending on configuration or if it's OpenShift or Kubernetes deployment. A pod is something like a virtual machine, has an interface, gets an IP address, MAC address, and finally has a plug into our VRouter kernel module in terms of the interface. Service is a concept of load balancing a whole bunch of pods. So if you launch 20 web servers and you want to give only a virtual IP address, you would instantiate a Kubernetes service which is backended by these list of pods for load balancing. Contrail has added our native load balancer to support this service, which means there is no proxying as such your ECMPing traffic to all those back-end pods. Ingress is when you're entering your Kubernetes cluster from outside to inside, in which case based on URL is one of the examples. You can say URL A goes to service 1 and URL B goes to service 2. We instantiate our HA proxy based load balancer. And the last thing is network policy which is currently in beta and will become GA I guess in 1.7 Kubernetes. We have implemented that using security groups. It's to control further isolation within a namespace, a group of pods talking to another group of pods and what are the controls in terms of pods and whether that certain whitelist is allowed or not. So Kubernetes by default works in, these are the isolation types and if you look at the top of the, the top of this diagram basically shows what is the default mode for Kubernetes. It's a flat networking model, there's no isolation. When you launch a pod, all pods can talk to each other, all services are reachable across. And this is something that we support by creating a single virtual network in Contrail where all IP addresses are allocated from a certain range and everybody can talk to each other. There's a need to actually create further isolation based on namespaces in Kubernetes which are equivalent to virtual clusters. So what we've added is a special annotation in the namespace resource. When you say openContrail.org slash isolation equal to true, we would create a namespace with its own virtual network. And what happens in that case is since every namespace which is isolated has its own virtual network, the pods launched in those respective namespaces cannot talk to each other. So you don't have to drop down to actually using directly network policies to isolate. You can do this at a much higher level by creating these namespaces in isolated mode and you're automatically preventing them from talking to each other. If you want to go further, even reduce in terms of isolation, you could actually use network policy for pods within the namespace. This is an example of ingress that I mentioned earlier which we've implemented using HAProxy. So in this case when you are trying to come into a URL with an external IP and your URL is XYZ.com going to slash dev, it is automatically filtered based on our HAProxy routing into service which is dev web service or a QA web service and so on. So we have a single service or simple fan out name based load balancing available for ingress. And on the back end when you go to service we actually use ECMP load balancing.  Now coming to deployment, I mentioned earlier that we do support many different deployment methods. What we are going to look at here is how we are using Helm to deploy Contrail. So step one, let me go to the next slide and come back actually. So the basic idea here is you have your bare metal cluster and this is a new thing that's happening in terms of deployment where Kubernetes is also becoming kind of something to manage your servers and all the control nodes. Step one is to go ahead and deploy Kubernetes on the bare metal servers. And after that we use Helm charts to deploy open Contrail pods. So in fact all of the Contrail components land up as pods in Kubernetes. In addition we also use Helm charts for open Contrail to deploy open stack pods and of course rolling upgrades and other features are also supported as part of these charts. So once you have the first two layers done, at that point you can actually create a, you can launch a whole bunch of VMs, you can take a set of VMs and create another Kubernetes cluster which is running in virtual machines. You can create an open shift cluster or you can have your standard virtual machines which are running on top of open stack. So all the blue VMs that you see you can decide to create your clusters as per your needs. The one component that I wanted to show on the right was Contrail controller. In this case you only need a single controller whether you're managing for your SDN needs for the nested Kubernetes cluster, for your open shift cluster and even for your open stack cluster. Single Contrail controller with the right credentials can manage every single SDN solution. So now let me just go back. So this is the deployment. Step one is we have deployed Kubernetes in this scenario. The next thing is we launch all the Kubernetes pods. So you have Contrail controller analytics analytics DB and we also need Contrail cube manager and Contrail vRouter agent is running as a demon set, Kubernetes demon set which means it gets deployed on every single compute node. So if you add another compute node or remove compute nodes because it's a demon set it'll automatically get scheduled and launched. The next thing is to go ahead and use an open stack Helm chart and that would bring up all of open stack components as pods. So at this point underline Kubernetes is actually making sure that all your control components be it Contrail or be it open stack are running and if there's any round time they will launch relaunch those pods and completely manage. So if slave one were to go down Kubernetes will ensure that all those pods will get scheduled on another compute node. So it provides resiliency and all that is taken care of by Kubernetes. So let me just go through a quick demo. We have the deployment already. You have to escape out of full screen. I don't know if you can see this clearly but so this is we have all the nodes here for this is our Kubernetes cluster with four nodes. I'm using the command Helm Ls so Helm and tiller are a combination to actually manage your Helm charts and in this case we have deployed Contrail as pods and you can see that all the pods in Kube system we have one controller pod which is actually running multiple containers all our controller containers and then we have the agent pods running on three compute nodes. It's the same thing in terms of the number of nodes but what I'm trying to show you is we have created another name space called open stack and open stack has all these services deployed via Helm. In addition what you can see is that all the open stack components are running as pods which were deployed by Helm. So all these pods have front end services so instead of accessing the pods directly they expose a service IP as I showed earlier and in this case you can see that we have the horizon service IP and that's the service IP that you would connect to. I guess we've already connected to that to get to horizon. So everything is being managed by Kubernetes both Contrail as well as open stack and that's what we wanted to show. We're running a little late I'll switch over to Travis. Thanks Rudra. So I have only a couple minutes but I wanted to share with you about AppFormix. AppFormix is a company that Juniper acquired back in December. It's a cloud operations product for managing both open stack Kubernetes and public clouds. Today I'm going to show you a little bit of the Kubernetes integration that we've done. AppFormix is designed to be extensible so that we can integrate with various cloud management platforms like OpenStack, Kubernetes, VMware, AWS. And what we do is we bring in the data and give you a visibility across all the layers of your environment. From the physical layer, the virtualization layer be it KBM or Docker and up to applications and services that are running on top of the infrastructure. At the top level you can get a snapshot of the entire infrastructure. We see here the worker nodes in this Kubernetes environment, the number of containers, the number of pods and a real time status of how these elements are meeting the SLA that has been configured by the user. So the user can set policy to automatically monitor and AppFormix does monitoring in a distributed fashion so that it scales with the size of the infrastructure. Policy is actually evaluated at the edge where the workloads are running so that we can do it in real time and send signals forward anytime we detect a condition that's violating the policy. Here it's easy to navigate across these layers. I can look at a single host, a single node and get a visibility into all the containers that are running on it. A snapshot is streamed of the resources on that host. I see all the containers, whether they're meeting the SLA in this case, one of them is not running. Therefore we're marking that it's missing its heartbeat. We can see which pod that container belongs to as well as the namespace or the service. So you can then cut across these layers. I'm at the physical layer. I can move up to the layer of a pod if I want to understand what's happening inside of a single pod. This is the elements or I could go at a higher level, a namespace, an entire namespace or a single replication controller. These are various aspects of which I can cut across the elements inside the infrastructure. Now, of course, just inventory is not useful. You also want to understand actual metrics. Although the agent that's running on the worker node is evaluating policy and collecting these metrics and evaluating them in real time, we do stream forward a summary of data for history so that you can interact as a user and see what's happening in the past over time on the host level as well as at the container level. So here you can see the memory usage on the host, the memory usage by each container, and we can then also create policy on top of that. So I can add a number of rules to monitor the containers and the hosts. And when I do that, it's a policy-based rule so I can select a subset of my hosts or I can select a subset of my containers based on the various groupings in Kubernetes, be it a namespace, replication controller service or pod level. If I want to monitor the Redis service, I can have a certain policy that will be in place. No matter how many containers are present inside that replication controller, they're all going to get monitored with the same policy as they dynamically scale up or scale down. FormX will push that policy out to the worker nodes so that they'll get monitored in real time. So that's a very brief overview of kind of what FormX can do, a bit of the monitoring aspect. It also does have some additional features in terms of reporting so that you can look at resource uses over time, figure out if you have the right types of resources or if you need to grow your infrastructure. And I'd be happy to talk with anyone about that in more detail at the Juniper booth. Thank you very much.


Welcome to the match reaction Liverpool won Everton Neal in the FA Cup. Everton crashed out of the FA Cup with one of the worst displays I think I've ever seen in a Masyside derby. Horrific. I literally gave it only just finished but I can't really get angry because you could see it coming during the game especially that first half. We were horrendous. We were absolutely horrendous and the book must stop at the players and some of the players, well not some of the players, all of the players today but just some of our players now just need to be dismissed as fast as possible and none of this idea that we can integrate them into a team. I'll just really just sum off. Jordan Pickford is garbage and needs to be moved on. Honestly, his mentality in games is just mind boggling. Before the goal went in, you know, this thing you can question whether he should have saved or whether it was an amazing shot, whatever, forget about that. Before the goal went in, he signed and knocked these little 20-yard passes on to people when the Liverpool players, the young Liverpool players full of energy are swarming round our players and giving them no time and space and what we needed to do was get out of our half and start chasing and turning them a little bit, basic football.  His reading of the game is absolutely abysmal and I get rid of him because I just think he's a joker in goal. Honestly, sometimes I look at him and I just think, who do you think you are? You've got absolutely no understanding of the game you're playing. I chase him, honestly. I think he's done. Every time he goes to Amfield, they just do something against him. They're always telling us how much they think he's the weak link and now I'm starting to think like that, I'll get rid of him. So he'd be the first one. Sheamus Coleman, his legs are gone, sorry, he goes as well. Sigarton, Snideland, gone, just get rid of them. Theo Wolcott, gone, get rid of them. They're straight off the bat and then you have these question marks all over the pitch. Not whether people are good players, just whether they can take that step up. I had a discussion with Baz here in the season about Robinson and Luca Dean and we had someone who was better and I said, well, it's Robinson because even if he's not as good a player, he'd run through a brick wall for you and he's got an end product. Luca Dean today, we've seen that all season, nothing, making poor decisions, giving away free kicks and getting booked, whatever. And we've got players like that all over the pitch, players who are rejects at other clubs that have come to Everton who can't step up, who are brain dead, who don't know what it is to be a leader in the team. And there's that all over the pitch. And today, for Carlo Ancelotti, he's just got the biggest wake-up call he could have of how bad we are and how bad some of these players are. Funny enough, people say, well, them putting out a weak side and all that, it was brilliant from Klop, absolutely brilliant for two reasons, well for three reasons actually. Number one, it put all the pressure on us and it asked us if we could handle that pressure. Simple as that. Number two, to inspire those young players and give them confidence to go out and play against Everton. He's been giving them a game all season in different things, league cup or whatever. Some have played Premier League, whatever. And the third reason, and this is the most important reason, fresh legs, fresh hungry legs, players all playing in the same system to what Liverpool play. And that brings a bigger question mark to me about the Everton Football Club.  Where are our under-23s that have won two titles in the last three years? Where are those players? Why do our under-23s play different systems to our first team? Now, the question might be stability. They've always been in charge a lot longer than the under-23s that anyone has done in the first team. But why hasn't Marcel Brans asked for there to be a blanket way of playing from top to bottom in Everton Football Club? Liverpool today have put four or five players in there, young players that all look like one at a time could be better than the first team. And they've all come together today. And they've chased our players off the pitch. And in the second half, they've come enough composure to just dominate the game. Let's not get it wrong. They dominated that second half. We didn't have a shot on target. So there's got to be question marks about that as well at the Football Club. The recruitment has been absolutely abysmal and we need to get rid of. We've been trying to get rid of five or six for two years. Now we need to get rid of another five or six. And I know this is what happens when you change the director of football and then change the manager. But there's got to be some long-time strategy. And I know people like Moise Keane, that's why he's brought them in. But when you bring people like Moise Keane in, you've got to put them in there with, you know, their competition can't be a 22-year-old. There's got to be some players in there who've got something about them. This is why I was calling for us to sign like Zlatan. And I know people like this may start. That's fine. I've got no problem with that. But it's for games like that. You've got to have someone on the pitch who's a leader. We've got no leaders in our club, none at all. None at all. And the only one might be Yeri Mina. And I don't know how good his English is. We just seem to be bringing in the same kind of player. People who are not hungry. People who have no desire. And people who come here because it's slightly better than where they were. And we give them a massive amount of money. That has got to stop on the car that one's here already. Because that was embarrassing. And there's 8,000 Nevitonians in there today. You know what? I don't think they would expect them more just because we're playing against the young players. I think they would expect them more because of the performances that we've shown recently. And you know what? I'm not going to use the excuse of the games I've caught up with them. In the first half we could have been easier if we scored three times. But we didn't. Because we don't have that mentality.  We simply don't have it. We swon around the pitch and it's all of them. With Charleston, Dominic Harville, Lewin, all of them, they're all included. They all swon around the pitch thinking it's going to be all right. Or they go the other way where they completely snatch your chances. There's no one in the middle who calms anything down. I think that's why he brought Delphon. But those legs have gone. They've gone. And that's the problem. We've got too many young players at one end of the scale. And too many players at the other end whose legs have gone. And not enough in the middle who make a difference. I'm in field today was absolutely abysmal. Absolutely. Slydlin and Sigarton. Oh my God. I couldn't get rid of those two players quick enough if I had my choice. I really couldn't. They are abysmal. Honestly, I couldn't get a centre of the field there. A centre to defend there. And put Hullgate into centre of the field. Or just couldn't get a centre of the field. But we've got centre of the fielders to come back, Gomez and Cobamon. Honestly, I couldn't get a centre back because we need one desperately. Put them in there and put Hullgate into centre of the field. I can't. Honestly, that's going to live with those players for a very long time. But it's going to live with the fans as well. It's going to live with the fans that we sent a team there with all the expectations.  Honestly, Liverpool, the way their players grew into the games, especially the young games, that comes from the manager. That's a confidence thing.  They all want to play. Will he will be champions of England and then champions of Europe, champions of the world and the universe and everything else. But we couldn't show enough bottle today. And do you know what makes it worse, right? If Liverpool had put that team out against a championship team or a league one team, I didn't think they would have got beat because that team would have gone for it and shown them no respect and be like, this is one opportunity to beat Liverpool and Anfield and they've put out the kids. How disrespectful is that? We're going to show them that kind of thing. We didn't. We go there and roll over because we've got a team of players. We've got no bottle. And it's as simple as that.  Because we just have this pattern. And you know what? In the past, I might have said, oh, it started with us as the fans. I think our fans genuinely believe we could get something today regardless. And we had a little go in the first half and then rolled over because we just couldn't score after hitting three shots directly at their keeper. And we deserved everything we got. And it's nothing to do with tiredness. And it's nothing to do with the players available. It's all to do with attitude and believing you can go somewhere and win. And that's what's kept Everton back, you know, poor players as well, I grant you. But that's what's kept Everton back from doing anything for the last 25 years is that belief that they can go and win in places. And I know that's been introduced by some managers or whatever. But until we change that mentality, this football club will not do anything. It will not do anything. And as I said, a team would have gone there today, a championship team or a league one team and would have done a lot better because they would have gone. This is our one chance to beat Liverpool and Anfield. And that was our one chance to beat Liverpool and Anfield. And we just rolled over and took it. And there you go. Abysmal and it should signal the end. I know it won't signal the end straight away for some players, but it should signal the end for five or six players. If you've broke all the ones you lost here, you've got to back them in the transfer market. I'm not asked about how much money we've lost or what this or whatever. If you want to be serious about this and you want to take the football club forward, you've got to back them. And that means going out and buying the players quality players that he wants in all the positions we need them. And of course you don't want to do that all at once because you find yourself in a situation where we've been in the last two, three years, but we've just got to go out and buy quality in the right positions. And some players who are proper footballers and not the botlers that we just seem to buy year in and year out, horrendous. I probably shouldn't be saying this, but well done to those Liverpool lads because they've had to go today and that's more than some of our senior pros have done. You know, our players who've played in World Cups and have played for internationals who just fall to bits, fall to bits when something is asked from them a little bit more than what we used to.  Do you know what?  Well fair enough, fair enough, but if it comes from our fans, our fans deserve to just tell them exactly, you know, because that was horrific, absolutely horrific, embarrassing. And I feel a lot worse. I actually feel a lot worse right now than I did when they put five passers, when they put the last minute goal last year. I feel a lot worse today, a lot worse because our players, well and truly bottled it, well and truly bottled it today. It was there for them to take and they bottled it. And Liverpool fans weren't even that arsed.  There you go. Let me know your thoughts in the comments. I'm sure it'll be full of lovely comments and stuff. But that's embarrassing, absolutely embarrassing from 1-11 embarrassing.  Some of their squad numbers, but you know, we've embarrassed ourselves. Let us know your thoughts in the comments, make sure to check out Baz's video, the player ratings. Give this video a like and if you want to subscribe and if you want to join us on Patreon, the links are in the description. Thanks for watching, see you later.


Welcome to All Hands Update, I'm Petty Officer Ian Cotter. The C&O and McPon recorded a new episode of Conversation with a Shipmate during a fleet engagement to the Pacific Northwest August 5th. The Navy's top officer and enlisted leaders stressed the importance of leadership within the ranks. They also discussed updates to the CPO 365 program and feedback from the fleet about the changes. They've embraced it and they've turned it into a great program. First and foremost it's about providing our first class petty officers with an opportunity to continue to learn and develop and doing it in an environment where we treat one another with dignity and respect. Their topics included integrity and updates to the senior enlisted academy. To watch the entire conversation, visit navy.mil.


How funny would it be if I just, you know, the chair snapped right now? Hey everybody, today we're going to be reviewing the Gamdias Achilles M1, which I'm actually sitting in right now. For those of you that don't know, Gamdias is a company based out of California that specializes in PC gaming equipment. They were kind enough to reach out to me and ask if I'd like to review any of their equipment and knowing that they had an RGB gaming chair, I couldn't help but ask and they were nice enough to send me one.  So hope you guys will understand that this is nothing but my uninfluenced opinion. So in this video, we're going to be covering four important things here, which is the assembly process, the functionality and the comfort, the actual look of the chair and then finally the price. So without further ado, let's get into the assembly process. All right. So I'm going to bring it over here now and let's get started. As you guys can see, this is a pretty big package. It is pretty heavy. So if and when you guys do order this, just expect for it to be very difficult to move this around by yourself. I think it's around 150 pounds, if that. Okay. So first initial thoughts from what I can tell here, all the styrofoam is protecting all the different corners of the actual chair. I'm actually so far impressed with just how well protected this thing is. Step number one, it tells us we're going to start with the wheels. All right. Sounds simple enough. So I have the base flipped upside down. It looks like I just popped the wheels in. It doesn't even look like I have to screw them in. OK. All right. That looks simple enough. It looks like once it looks like once you pop these things in, they're not really coming out. So this little cover here for the wheels is to actually block off all the different spots because it looks like this chair was welded together.  That's a nice added additional design. Step number two, it looks like we get the base of the chair and we have to remove bolts before attaching mechanism base support and armrest. All right. Yeah, it's got to be this way. OK. If you're getting the Achilles M1 model like I am, it's kind of not super intuitive, but it is also at the same time the hole lines up kind of at the same angle with how the bottom of the chair of the base is facing. So the poles going that way. OK, so now I'm unscrewing the four screws for I think the left armrest and then I'm going to do the same thing on the right side. And then I'm going to screw them all in. Then I think I'm ready to move on to step number three. In hindsight, I should have definitely unscrewed and installed the armrest before I did the base mount for the seat of the chair. But like I just showed you, it's not impossible to still do. It's just like slightly in the way, not that big of a deal.  OK, so now we're completely done with step number two. And now we're moving on to step number three, where we connect the metal pole from the base of the chair to the wheels. So there is actually nothing, you know, that you screw in. It just looks like because of the way the metal shaft is shaped that the wheels will actually stop automatically and can't get pushed any farther up the pole. So it looks like now looks like now we just flip this thing over. OK, so it looks like these two are the levers that actually control the reclining aspect of the chair. And this one is just loose, kind of doing its thing. And this one here on the right, it looks like it's controlled by this lever. Yeah, it looks like if I pull this crank up, it should let me pull the chair back. Well, I'm going to go ahead and screw in the top part of the chair and see if that changes. So before we screw this part in, you'll actually notice here at the bottom of the chair is where the USB cord is sticking out, which is what I assume we have to plug into the computer. And in case you're worried about it being too short, Gambia also sends a USB extension cable. So you don't have to worry about buying one of those. You got to unscrew the side bolts first. OK, so now that we've unscrewed both sets of screws on the side, we're going to go ahead and slide this thing in to the pre cut holes. And now we are going to screw all of them back in. OK, I just figured it out. So quick tip, when you're screwing these screws back into the sides to get the backrest on there, you actually can't just do it with it slid on like you think you can. What you have to do is you actually have to pull this chair a little bit farther back, because when you slide the backrest on the two mounts on the base of the chair, it kind of leans forward too far.   Yeah, there we go. Yeah, let's see. One, two and three. Oh, yeah. Oh, yeah. Whoo, this is nice. How funny would it be if I had to do that? How funny would it be if I just, you know, the chair snaps right now? But yeah, in terms of comfortability, this thing's this thing's pretty solid. I mean, if you're taller, the armrests get up there. If you got like a lower desk, you put them down here. But this is this is pretty nice. I definitely like this. I don't feel like I'm restricted. I got plenty of space to move around if I want to like hunch over to this side or hunch over to this side. You haven't really have any complaints about this. This is nice. The wheels seem like they move pretty decently.  Whenever I like slightly want to adjust, I kind of take off across the floor. And this one doesn't do that, which I'm actually, yeah, I like that. I like that this has like a nice clean wrap here on the side. It's got a nice little pattern. As far as like functionality goes, this chair is pretty nice. But you know, obviously the point of getting an Achilles M1 would be the RGB. So we're going to actually go and take a look at that right now. So let's go. OK, I think this thing looks pretty sick. It's kind of a shame that you can't see it while you're sitting and actually operating on the computer, but it's definitely as spectacle. This thing is this thing looks pretty cool. You should be able to control these lights. I'm actually going to go in and try to operate this chair now and see what kind of different patterns we can get out of this thing. OK, so the software is called Hera. It's H-E-R-A. You can find it pretty easily on their website. They don't have a lot of downloadable content and it looks like you can control this a bunch of different ways. I guess I'll go through this together with you guys. OK, so there's there's breathing. There's neon. Blank seven color wave, random light, rotate static, run seven wave and cross. And yeah, those those are the options. I think my favorite is definitely going to be wave and I'll turn the brightness all the way up and the speed. I want to see what that looks like. In my opinion, I think this thing looks great. I'll turn around now. So to wrap this review up, let's go over the four important points. Number one, the assembly process on a scale of one to ten, with ten being the hardest, this overall build process for the chair came in at a three. I will definitely reemphasize like I talked about earlier in the video that actually screwing the backrest into the supporting levers on the side was definitely not the easiest thing. And it took some fidgeting around before I could actually get it to work. But other than that, putting this thing together was a breeze. Number two is functionality and comfort. And I will honestly say that I find this chair to actually be slightly more comfortable than my Odyssey gaming chair. There are two major reasons I say that. Number one being that this chair actually has better ventilation for long periods of sitting. So if you do sit in your chair for long periods of time like I do and you do sometimes get leg sweat, I've used this chair for the full day now. And I haven't had that issue like I have with my Odyssey chair. Number two is that the pillows that actually came with the gumbiest gaming chair are actually a lot more comfortable than the ones that came with my Odyssey chair. I would definitely say when I use this thing, I won't be using the head pillow just because I like to have my head farther back. But for the lower back support pillow, I can definitely see myself using this long term. And for the rest of the architecture of this chair, I wouldn't say that it's any better or any worse than my Odyssey or any other gaming chair that I've experienced. It's actually very identical, but I would definitely say that the material that this is made out of the ventilation as well as the backrest pillow is better than anything I've experienced. So in terms of functionality and comfortability out of 10, I would definitely give this chair an eight. Number three, the overall look and aesthetic. This chair is a little bit slimmer than most gaming chairs. And I would say when I personally am looking to get one, if I'm looking just for the look, I do like something a little bit thicker and a little bit bulkier, but it's definitely not so thin that this is going to get confused with a larger office chair. And as for the RGB lighting, I would definitely say that I am a fan. That doesn't go without saying that in the future, I would definitely like to see some company out there work in the RGB lighting almost into the stitches and kind of have just like the full architecture embedded with LED lights. But the fact that GOMDES has actually gone so far is to just incorporate the RGB lighting into this chair in general. I definitely think that it makes it stand out from the competition. Earlier in the video when we went through the different patterns that this chair actually had because of the lighting that I had projected onto the chair, it definitely didn't do many favors for it and make it look as good as the lights actually do look in real life. I turned the lights out for the shot that you're going to look at right now. And honestly, I would say that the lights on this chair do look amazing, especially if you have it in the right lighting. Unfortunately, you'll never actually be able to see the RGB lighting when you're sitting in the chair, which I think is kind of an interesting design.  But overall, all things considered, when I look at the stitching, the lighting, the actual face and body of the chair, I would give this thing an eight out of 10. And finally, the price. The Achilles M1 comes in at just over three hundred dollars and you can find it at New Egg, Best Buy or Amazon. And don't worry, I will put links in the description. Now, if you're one of those people that just desperately wants to gaming chairs just to say that they have one, yeah, there are some chairs out there that are just over a hundred dollars that aren't brand name and have OK made quality. But if you're going to be looking at a chair like this or other brand name chairs that other streamers and professional gamers use, they all actually tend to cost around the same price point for the Achilles M1, which is just over three hundred dollars. So if you are an RGB fanatic and PC gaming enthusiasts like myself, then why not get a chair that actually comes with the RGB lighting, because most chairs that do cost just over three hundred dollars do not come with that if not all of them. So taking into consideration that this chair does come with the additional RGB lighting feature and is priced around what you should expect to pay for a brand name gaming chair, I'm going to give this price a six out of 10. So that wraps up the review. If you have any questions on this specific model, go ahead and leave them in the comments below or if you just want to let me know your thoughts or if you're going to even buy one, go ahead and leave those in the comments. I appreciate your time. And as always, thank you so much for watching and have a great day. Oh, yes.


Item number SCP-504 Object Class Safe Special Containment Procedures All seeds, plants, fruit, crossbreeds, and other products of SCP-504 to be classified as SCP-504. SCP-504 seeds need no special containment other than to prevent misuse by unauthorized personnel. Grown SCP-504 plants and their fruit should be kept in soundproof rooms. Guards and researchers assigned to maturing or growing SCP-504 to be equipped with radio-enabled masks which insulate non-transmitted sound and are to be instructed to avoid attempts at humor. Description SCP-504 is a species of tomato physically and genetically identical to that of the typical commercially grown tomato. It was recovered in ██████, Kentucky, after a woman reported to the police that her farmer husband had been murdered by his lunch. The Foundation is currently working to identify and destroy loose strains of SCP-504 and the surrounding commercial farming areas. When a poor attempt of humor is made verbally within human hearing range of SCP-504's tomatoes, they instantly accelerate to a speed of at least 100 miles per hour, or approximately 160 kilometers per hour, 45 meters per second, in the direction of the sound source. Only mature tomatoes separated from their vines in less than 10% rotted or chemically compromised exhibit this effect once each. Tomatoes do not have to be physically intact, though ingested tomatoes are usually insulated enough from sound to prevent their effects before neutralization by stomach acid. SCP-504 tomatoes seem to reach speeds relative to their inciting attempt at humor, C-experiment log. Relevant variables seem to include cornyness, humor to length ratio, and use of puns. Language appears irrelevant. Note Whoever snuck SCP-504 into the cafeteria kitchen is getting terminated.  Dr. Blast Log of Test with SCP-504 Item 1 Mature SCP-504 Tomato Subject d504-1 Spoken It's a hippopotamus, a hippopotamus, or really just a cool opotamus. Result, no change of velocity. Item 1 Mature SCP-504 SEP-504 TEMETO SUBJECT-D-504-1 Spoken What's an archaeologist? Someone whose career is in ruins. Result? Tomato clocked at 124 mph. Subjects suffered a broken nose. Note, it appears that SEP-504 has a certain taste in jokes. This might indicate sapience. I hope not. Dr. Blast Item ██ 1. Mature SEP-504 TEMETO SUBJECT-D-504-2 Smoking, three tomatoes are walking down the street, a papa tomato, a mama tomato, and a little baby tomato. Baby tomato starts lagging behind. Papa tomato gets angry, goes over to the baby tomato and smushes him and says, catch up. Result, tomato clocked at 264 miles per hour. Subject rendered unconscious. Item, one mature SCP-504 tomato. Subject D-504-3. Smoking, so, I was just going to bed and my brother told me, good night.  Good luck on a healthy dermis. Result, two second pause before activity. Tomato clocked at ██████. Sound barrier broken. Subject killed. Item, three mature SCP-504 tomatoes, each from a different crossbreed. Subject D-504-4. Smoking, if you have dentures, don't use artificial sweetener because you'll get a fake cavity. Result, all three tomatoes clocked at exactly 145 miles per hour. Subject injured, two teeth dislodged. Item, one mature SCP-504 tomato, split into quarters. Subject D-504-5. Spoken, I tried to walk in the target, but I missed. Result, all four pieces clocked at 212 miles an hour. Subject severely injured, right eye destroyed by piece of tomato. Item, one mature SCP-504 tomato, subject. CD player playing harmful as swallowed, 2003 by Dane Cook. Result, at ██████. Tomato clocked 167 miles per hour, CD player destroyed. Notes, it worked with recordings. Damn it, didn't even have to deal with Class Ds in the first place, Dr. Blast. Item, three mature SCP-504 tomatoes, one to reach test subject. Subject. After the introduction to the following news item, bomb blows hole in linen statue, the three following jokes were made. Test subject 1. Oh, that's gonna leave a marks. Result, tomato number 1 twitched but did not displace from its original location. Test subject 2. BBC is just stalling the good news. Result, tomato clocked at 152 miles an hour, chip tooth and hairline jaw fracture. Test subject 3. Blows. Result, tomato clocked at ██████. Subject is hospitalized with a massive skull fracture. Notes, I thought we'd just established that recordings work in place of live subjects.  Poor guy might not even recover before termination rolls around. But I'm making it clear that whoever oversaw this route of testing is getting a serious reprimand. The same goes for whoever leaked its video logs to the staff. Dr. Blast. Item 1. Mature SCP-504 tomato. Subject 2. Television playing the Saturday Night Live Sarah Palin and Hillary Clinton skit. Result, tomato reacted as if confused. Slow motion video shows three separate bursts of speed in excess of 200 miles per hour, two instances of motion at normal throwing speeds, and one unprecedented instance of backward motion, all in one trajectory. Dr. King hypothesized that the tomato was unsure whether or not to take it seriously. Item 1. Mature SCP-504 tomato. Subject, a portable computer playing a pre-recorded engineering joke. Transcript, 2009 is going to be a complex year. We already know the real part, we still have to find the imaginary part. Result, supersonic blast detected. Computer was completely vaporized by the tomato's kinetic energy. Computer readings indicate an approximate speed of 2,174 miles per hour. Item 1. Mature SCP-504 tomato. Subject, a portable computer playing a partial audio recording of the Monty Python sketch, the funniest joke in the world. Transcript, 2010 is going to be a complex year. Result, tomato explodes debris clocked at 137 miles per hour. Computer heavily coated by debris, keyboard ruined by exposure to liquid matter, all other components proved functional after cleanup. Item 1. Mature SCP-504 tomato. Subject, a portable computer playing the text of SCP-904. Result.


Hey guys, welcome back to my YouTube channel. This is Daniel Rosal here. I've done a few videos on this channel today about my various border spotting escapades here in Israel. I've kind of had a fascination with borders ever since I was a kid. I went to Nicosia in Cyprus, which has a big and very prominent border running through it. And since then borders have kind of been of interest to me. They're also a good way to explore the kind of peripheral parts of Israel that folks often otherwise don't visit. If you are by any chance also interested in borders, check out my videos on Hunan Castle in the north of Israel, which is a really good place to see the Lebanese border, just about as close as you can get as a civilian, because that's considered a very, very tense hostile border. So the army for very good reasons doesn't let you go too close to the actual border, but you can see it. And you can also see it from Matullah, the northernmost town in Israel. You can get really, really up close to the fence there.  So it really makes an impression about how small this part of the world is. The one border I haven't done much exploration of is Israel's border with Egypt, which is, of course, Israel's southern border.  A number of years ago, and it's probably best known in Israel as, unfortunately, being the border through which there is a lot of human trafficking and drug trafficking less so since they built a big fence on it. But that is the border. It's located along the desert, literally. So it's a desert border with desert on both sides of it. And I heard from friends there is a road you can drive on during special occasions, let's say, when the army allows civilian traffic. And that is called Route 10 in Hebrew Kvish Esser. And I wanted to just do the short video for those who are thinking of doing this just to give a little bit of info in English, because there are lots of videos in Hebrew, mostly a few in English, driving on the border. But I wanted to just point folks in the right direction if you're interested in this sort of thing for an expedition. So the resources I found are really mostly in Hebrew. So you should, if you are interested in doing this and knowing when it's accessible, type into Google Kvish Esser and you will get a number of informational resources like this one from Negev Tours. This is a this is a crazy video. And this is showing what it is. It's basically a narrow road, typically used. It's every border in Israel, whether it's the Lebanese border or the Jordanian border has a road or the Gaza border or the de facto border with the West Bank typically has an army only road right next to the border. Typically, you can't go there as a civilian. There's signs saying army only. So Kvish Esser is one of those roads. You can see it's a little narrow track right by the border friends. But unlike the other borders of Israel, they army, I guess, because it's a relatively calm border, given that there is a peace treaty with Egypt. They do let civilians drive on it on specific dates. So there is lots of quite a decent amount of info about it here in Hebrew. They do warn that there aren't like gas stations for and is quite a long stretch of road through the desert. So you want to make sure you have a full tank of gas before going there. And you also need to check the dates. It's open in advance. So by searching for Kvish Esser, you should find these dates. These are the dates that the border road is open for, I believe, yeah, twenty twenty two and they give you a little elevation guide as well, as well as a phone number to call for the army department. So the deal is that you can drive on it during the dates. But if it's not in the dates, you either can't go or you have to ask specific permission for the army. I've no idea whether they give out these like exceptions easily. But there is a phone number there that you can contact. And they do actually answer the phone. I've called them and they'll even confirm the open dates with you as well. So they're pretty helpful. Here is another blog with some cool photos of the border road Kvish Esser. You can see an Egyptian army post on the Egyptian side of the border there. They're pretty distinctive looking as opposed to the IDF post. They have like different coloring and all that.  What else? Now the route of Kvish Esser, just for those curious, I'm going to do a little bit of a Google touring here. And just just to see, show you where it goes, because they don't always open the whole road at one time. So sometimes it's sectioned, so it's useful to know the geography. So this is a last in the south of Israel. This is Tabba border, land border crossing going into Sinai, which is an interesting experience to cross there. And coming up northbound from Elat, you have Route 12. You actually have to kind of zoom in to see where Route 10 starts, right? It's this little white road here and there's a junction here. I'm sure it has a name. I'm not quite sure what the name is, but you can see 12 forks off to 10.  Now, if you turn on a navigation layer, we might be able, it might be a little bit easier to see and you can see that it's a desert. And then it continues all the way north, north, north, north, north. You can see Route 10 here and I'm going to zoom out a bit so this doesn't take forever. The only really town there's a monument here. The first town you're going to hit is Nitsana, which should be coming into view. And there's a road on the Egyptian side of the border as well. You can see the Taba Rafa Road. Rafa is in the Gaza Strip. So it comes a little bit away from the border. There's a little bit of kind of skirting and then we're right back to the border itself. Nitsana, I believe there is a land border there, a land border crossing, but it's not in regular use. So Taba is for commercial goods. Taba these days is the only land border crossing between Israel and Gaza. Here we go. And here is Nitsana. So that's the only really sort of notable town on the Israeli side. I don't think there's really much on the Egyptian side. And then if we can continue further west, north, yeah, northwest, just for a little bit longer, you'll eventually hit the fence with the Gaza Strip. This is the Gaza Strip and Keren Hashalom. And at this point, 10 ends and it turns into right two, three, two going north along the Gaza border. And this is a checkpoint here. So you can continue past this past this junction. So that is a return for those interested in a bit of less typical off the beaten track exploration in Israel. If you are interested in doing this, you should I use your Hebrew and put in 10 into Google and then make sure that you check the dates. That it's open. If you want to double check, you can call the army. Or if you're looking for permission to go in during during something else, check the army and pay attention to all those notifications regarding the fuel, because probably the last thing you want to happen is to run out of petrol or gas while you're on a tiny army patrol road in the middle of the desert, in the middle of the summer. That does not sound like fun to me. If you're thinking about doing this expedition, I hope this was useful. I am doing this expedition again at a unspecified point in the future. And I will be posting some videos from the little trip. Thank you guys for watching more videos for me on the usual miscellany of subjects coming soon to this YouTube channel.


Hi, I'm Zor. Welcome to Unizor Education. This lecture is a continuation of the topic related to trigonometric representation of complex numbers. In this particular lecture, we'll talk about exponentiation of complex numbers in trigonometric form. And obviously, this is part of the whole course of advanced mathematics presented on Unizor.com, where I actually suggest you to watch this lecture from, because the site contains, for every lecture, there are notes which basically serve as a textbook. Well, besides, obviously, there are exercises and exams, etc. Alright, so we continue talking about trigonometric representation of complex numbers, and we'll talk about raising into power. Now, last lecture was very much introductory. I was just talking about how the complex numbers are represented in trigonometric form, or polar form, if you wish, which looks like this, where r is an absolute value, or modules, and phi is the argument or a phase of the complex number. Now, raising into power, obviously, it's based on multiplication. And multiplication, as we know from the previous lecture, is very easy to accomplish in polar coordinates in trigonometric form, because if you have two different numbers, r1 and r2, cosine phi2 plus i sine phi2, then their multiplication is very easily expressed in this format. You multiply the modules, and you add the arguments. Now, analogous formula of multiplication in canonical representation looks much more complex. It's AC minus BD as a real part, and complex part is BC plus AD. It's a little bit more cumbersome, and you can't really remember it quite well, but this is a very natural, and it has a geometric representation. Remember, if r1 and r2 are equal to 1, then basically we are just turning the point on the unit circle, which is represented by this particular representation, where this is the angle of phi1. We are turning by angle phi2, getting phi1 plus phi2. So, multiplication on the unit circle with r1 and r2 is equal to 1 is basically a turning rotation by this particular point. Now, this is multiplication, and as you see, it's easy, and that's why it's very easy to define the power. Now, we will start with, obviously, natural power, integer positive power n, and what does it actually mean? Well, I would like to make a very interesting comment here. What we are talking about, we are talking about certain things which meet the definition. Like, for instance, if we are talking about multiplication of the real numbers, we start with multiplication of integer numbers, actual natural numbers, positive integer, then we add the negative based on certain properties of the multiplication which we would like to preserve, and then we expand the irrational numbers, then the irrational numbers, and same thing with any other operations. First, it's defined for a simple case, and then we examine the properties in that simple case, and we are trying to define for more complex objects in the same manner to preserve these properties. Now, what are the properties of the exponentiation, of raising into power which we would like to preserve? Well, obviously, we know that something like this. We did prove this for rational numbers, actually for all real numbers, but let's talk about rational numbers, where m and n are any rational numbers, right? And a was a positive number. Now we are talking about complex numbers and raising the complex numbers into certain powers, and that's not easy, obviously. If you remember, within the real numbers, we did not really even allow the negative numbers as a base, primarily because we cannot raise minus one into power one-half, which is actually a square root. In complex numbers, we can allow even that, because this is equal to i in the complex numbers, right? Because i-square is equal to minus one, by definition. Again, we are defining, we are expanding our universe, but we are trying to preserve the good properties which we already observed in the smaller universe which we had before. So, now we are expanding to complex numbers, and we would like to preserve properties like this, and properties like this, and properties like this. So, these are very good properties of the exponents as they are defined in a simple case with real numbers, or even with integer numbers, if you wish, even with positive integer numbers, because that's where it comes from. It comes from the positive integer numbers where all these are obvious, right? Because positive integer number raised into positive integer number is basically a multiplication by itself, m times and m times, which is actually m plus n times, right? So, for a simple case, it's obvious, and then we expand the universe to preserve these properties. I'm going to preserve these properties for the complex numbers in trigonometric form, and I will define these operations correspondingly. And again, let me start from something simple. And simple is where we are talking about raising the complex number into positive integer power, which is basically multiplication by itself and times. And we know how the multiplication looks like in trigonometric form in polar coordinates, right? So, if I have r times cosine phi plus i sine phi, if I want to multiply by the same number, I will have to multiply my absolute values, right? And I have to add the angles, so phi and another phi, so it will be 2 phi, right? So, that's the formula of raising to the power of 2. Now, how about power of n? Well, obviously, it's a trivial exercise in induction. You can define, you can actually prove this by induction. So, this is, for n is equal to 1, that's basically an identity, right? Now, for n is equal to k, if we assume it, then n is equal to k plus 1 would be the same thing for n multiplied by this single expression, right? And that means that we will have to multiply the absolute value of one times another, which is r to the n times one more r, or r to the k plus 1. And this will be k and again plus 1, so it will be k plus 1. So, the formula is trivial proven by induction. Okay, so that's fine. This is trivial. Now, let's expand it to different values of exponent. First, let's talk about negative exponent, right? So, let's say we want to do this. We want to define it in some way so it's reasonable. And all the laws which I was talking about before are supposed to be preserved. Now, how can we do it? Okay, let's just think about exactly the same way as we were talking about the similar problem in real numbers. What I did was, I used this property. Now, what if my n is equal to minus m? I will have a to the power of m plus minus m is equal to a to the m times a to the minus m, right? According to this formula, if I would like to preserve this property, this must be true. If I want to expand to negative exponent. Now, what is this? This is a to the power of 0, which is, again, there is a property of being equal to 1, which means that this a to the minus m is 1 over a to the power of m. And this might be a definition. And if this is a definition of negative exponent, then everything is fine. All my rules, laws, whatever properties are preserved. Now, I will do exactly the same thing here. So, I define this as 1 over r times cosine phi plus i sine phi. Okay, right? So, that's easy. Now, let's think about how I do this. Well, 1 over, yes, to the power of m. Now, 1 to the power of, 1 to the r to the power of n is retained. But now, I have to express this somehow in a power of minus m. Sorry, the power of n. Now, let me go to the properties of multiplication of the complex numbers in trigonometric form. What do I know about this? Well, I already know that this is equal to cosine n phi plus i sine n times phi, right? So, here I can replace it with this, n phi n phi. Okay, fine. So, let's talk about this. For instance, I have this expression. What if I will multiply it by this expression? What happens? Well, we know that if I'm multiplying two different complex numbers in trigonometric form, my absolute value is multiplied, which is 1 and 1. But my angles, my phases, my arguments are added together. So, what will be, will be cosine of sum of this, which is 0, plus i sine 0, which is equal to, now this is 1, cosine of 0 is 1, sine 0 is 0, so this is equal to 1. So, what follows is that 1 over this is this. So, I can replace this with this. And to be even more explicit, I will use this. 1 over r to the n is r to the power minus n. That's the real number's power, right? So, what do we have right now? We have this same exact situation. I have this exponent, which is negative. And the formula basically looks exactly as if it was the positive. So, I raise my absolute value to this power, and I multiply my phase, my argument, by this power as a multiplier. So, the formula is exactly the same as just a second ago I was talking about for positive integers. So, that's quite interesting actually. The formula is exactly the same for positive and for negative. You raise the argument, sorry, the absolute value to the power, and you multiply the argument by the power. Okay, fine. How about rational? Well, let's start rational slowly. Let's do only rational as 1 over n. So, my purpose is r cosine phi plus sine phi to the power 1 over n. How can that be defined properly? Okay, well, let's just think about, let's take this and raise it to the power of n. What happens? We don't know how to raise to the power of n, right? We just used it, regardless, by the way, of the fact whether n is positive or negative. We have to raise this absolute value, the modulus, to this power. So, r to the power of 1 over n to the power of n would be what? We have to multiply, right? This is r. So, the result would be, the absolute value would be r, and the face, the argument, I should multiply my angle, my face, by the power, right? So, it would be cosine phi over n times n plus i sine phi over n times n, right? Now, what can we say about this? Well, if this to the power of n is equal to this, now, by definition, what is 1 over n? It's a number which is being raised to the power of n would give me this one, right? If I will raise this to the power of n, my powers are supposed to be multiplied, right? It will be 1 over n times n, which is 1, which is just exactly this piece. So, what I can say from here is that this is equal to this piece. Since, as I just said, if I multiply, if I will raise this to the power of n, I will get this, which means this raised to the power of 1 over n will give me this. Now, again, let me repeat, these are definitions. These are not theorems. They are definitions of new operations, how to raise the complex number into positive integer, to negative integer, to irrational power. Now, irrational would also be nice, obviously, to complete this particular thing. Well, that's a little bit more involved. And as I was explained in the irrational power of real numbers, real positive numbers, actually, you have to really use the limit theory. And every irrational number can be considered as a limit of certain sequence of rational numbers. And basically, the approach should be exactly the same thing. So, you can define the irrational power as a limit of rational powers where the rational powers tend to the irrational number if there is one. All right? So, these are formulas for raising this particular complex number in trigonometric form in any power. We had integer positive, negative, we had this one. Now, I would like to, again, point that the form, exactly, the form of this formula is exactly the same.  So, it's exactly the same formula. Now, the last one which I would like to add is to put m over n here, right? Now, what happens in this case? Well, these are just two different rules. You have to apply them sequentially because what does it mean if you do m, m over n? You can consider it as a to the power of m and then to the power of 1 over n, right? Or vice versa, first to the power of 1 over n and then the result would be the power of m. So, you're applying two different formulas. One formula gives you, let's say, we are considering this as 1 over n and to the power of m. I have too many parentheses and brackets, etc. So, I have this to the power of 1n and then to the power of m. Now, what is this? Okay, first we raise it to the power of 1 over n to get this one. Now, this I have to raise to the power of m and I get what? My absolute value is supposed to be raised to the power of m, which is this. And my argument is supposed to be multiplied by plus i sine. So, again, you see exactly the same formula. You raise your absolute value to the power, whatever the power of the whole complex number is, you use this power as a multiplier for the face, for the argument, right? So, in general, I can basically derive this formula for any kind of power, any kind of real power. Integer, negative, rational, irrational, r times cosine phi plus i sine phi to the power of x, let's say. Where x is any real number is r to the power of x times cosine x phi plus i sine x phi. That's better to use brackets here. So, this is a general formula for all real x. Now, and that's very important right now, you see, in trigonometric form, that looks quite easy. Try to do it in regular canonical representation like a plus bi. Even this, something like to the fifth degree, even this would look extremely complex because you have to multiply a plus bi five times by itself. It's a lot. It's a to the fifth degree and etc. I mean it's a big formula, which obviously nobody remembers. But in the trigonometric form, in the polar form, that's raising into any kind of a power, the operation of exponentiation, raising into power, looks really simple, right? Well, and that was my point actually for today's lecture. What I suggest you to do is go to this website and read the notes for this lecture. It's like reading the chapter in the textbook, just to make sure that you properly understand it. So, what do we know right now? We know that we can use any kind of an exponentiation to a real power for complex numbers. So, if something like minus one to the power of one half was impossible to do in the realm of real numbers, in the complex numbers, it's very easy to do. What is it? Let me just, you know, make an example. Minus one is here. So, it's one times cosine of the angle of pi plus i sine pi, right? So, forget about one. We don't need it. Now, I'm raising it to the power one half, which means what? Absolute value is one, so it doesn't matter. I will have cosine pi over two plus i sine pi over two. Now, this is zero, right? And this is one. So, I have i. You see, i to the power of two gives me minus one. Square root of minus one is i. So, in complex numbers, it's easy. Okay, that's it. Thank you very much and good luck.


It's chart by chart, it doesn't make a difference, you know, if the market does have a day to sell off tomorrow, it's not going to make a difference. If one goes down, they won't go down, right? Welcome to Access a Trader, the number one community for those who are committed to taking control of their trading in order to achieve success, profitability, and longevity. Thank you for joining us. Here's Dan Shapiro to help you find your edge, master your process, and own your future. Hey guys, good evening everybody. Welcome to another edition of the Access a Trader.com Nightly Wrap-Up Show. I hope everybody is doing okay. Hell of a day, right? Hell of a little sell-off we've had here. Going into today's session, we talked about how that bounce yesterday, you know, really did us no favor today. There was no really technology names that I was sitting there today, I go, wow, I got it on. Because again, when you have a deck, well, I don't want to call it a dead cat bounce. But when you had a bounce yesterday, the initial test of the 50-day moving average, it left a lot of charts in the middle of the ranges. So last night's focus was away, right? Away from technology, especially to the long side. And we talked about names, you know, that we talked about names, other names, right?  They were very, very aggressive names, you know, names like Oil Names, Oil Names had a second run before a pre-aggressive reversal. And we talked about yesterday, the banks, what was the last time the banks had a two-day run? And again, so everything started slowly butchering, souring, right? Very by little, you could see it over and over and over again. And the names that were weak yesterday, the technology names that couldn't rally, it had that, you know, pretty good aggressive snapback into the close because the queues held the 50-day moving average starting getting weaker and weaker and weaker. Now the question was, well, what was going the Fed kind of give us some new clues, right? They've been talking about interest rate hikes for three years. And every single time they're about to do it and they even announce a day they're going to do it and a month they're going to do it and the second they're going to do it, all of a sudden the game plan switches, right? So every rate hike that was supposed to be imminent for the last three years has been pushed back. And kind of here we are now. So there was a lot of weakness initially today in the NASDAQ. You could just see it. NVIDIA was super weak, you had Facebook super weak, Apple was reversing, more put by and coming, Amazon never really rallied. We talked about Amazon yesterday in the close, even beyond, right? Remember that chicken headline that we talked about last night? Again, who the hell is walking into a Kentucky fried chicken, okay? And ordering fake chicken. I'll wait. We'll talk about the pivots in a second. But the most important part was what was going to happen with the Fed? And the Fed came out basically of every hawkish stance and they're saying, well, expect another rate hike, right, well, excuse me, a rate hike in March, okay? We'll shall cease at the blind man, okay? This has been going on for years and years and years. So until we actually get a rate hike, their only dude is literally talking about a rate hike. But it got the market nervous. It got the market jittering. Obviously, the whole COVID thing is not helping anybody out. Everybody knows somebody who knows somebody who knows somebody else, including themselves that it's probably sick from this thing. We all agree, probably you're not going to die from this thing.  And yet everybody's sick. So what happened today after the Fed got really, really aggressive, right? You could start seeing really big money being put down on the option side and the put side of a lot of your favorite technology names. You had NVIDIA, when NVIDIA was at 293, 293, they were coming for the 275, 270 puts out of nowhere, right? Short-term expiration. When the video was taking out yesterday's channel below this 283 level, they started coming for the 275s, very, very aggressively as well. Amazon, right? They just never rallied, just never participated in any rally here in the last couple of weeks, finally closed below this whole macro range. Again, this is not a good thing, right? Again, we all know, we all agree that Amazon's going to be at 5,000 one day. It's probably not going to be at 5,000 tomorrow. That's the most important part is what we can see and we can catch on day to day. That's the one thing. But the craziest part about it is, I saw so many stocks. Again, tonight, I could have easily, if you did your research tonight, right? You could literally, any stock you want, right? Any stock you want that closed below rising daily support, you could put it on your watch list for tomorrow's day two selling. Now, the question is, is there going to be day two selling, right? Or at least aggressive selling continuation from today's move? That's the million dollar question, right? Nobody knows. Is it possible we get a dead cat bounce tomorrow? Because again, you got a 3% decline today on the NASDAQ 100. That's kind of a big deal. 3% on one day is a big deal. And the most important part is, which stocks are going to continue to go lower? Now, if we do have a dead cat bounce tomorrow, I have zero, absolutely zero interest on the long side. There's not a chart out there that I'm going to turn around and go, wow, this thing looks really, really good when you have the masses looking like this, right? And I looked at a chart, like for example, like Netflix, Netflix is approaching its 200 day moving average. Forget about being rejected off the 50, this, that, the other thing. This thing is approaching its 50 day moving average. You have Facebook that lost its 50 day moving average. You have Apple, who's been the pillar of strength, closed literally right, right? Closed literally right on its upper trend line, okay? If this upper trend line loses, we started seeing really big aggressive 170 short term expiration in Apple. So if Apple starts leading the way, you know, this thing, you know, the market can really start escalating if you have rising rates and you have, you have a correlation disconnect if technology moving lower. You've got names, for example, like Microsoft, I mean, look at this move on Microsoft approaching really, really exaggerated support here. So again, it's going to be very, very important for the bulls tomorrow, especially if we get a washout at the open, if we get a gap down, the bulls really need to reclaim, right? They really need to reclaim macro levels and if it's going to be, if you're going to get a reversal tomorrow, it's going to be a very, very big if, but if you are going to get a very, very big reversal tomorrow, we have to have a down open. We have to have a down open, throw the baby out with the bathwater. You want to make sure that retail is screened and no masks, right? Hanging the white towel is saying, I don't want to be in anything, sell my stocks at every single level. I just don't care. That's where you're going to get your reversal. The worst thing we want to see, if you're a market participant, especially on the buy side, right?   If you get a gap up tomorrow, there's a high probability whatever stock you're looking at is going to get stuffed right at 60 minutes supply and reverse course back to the downside. If there is a bullish type of dead cat bounce tomorrow, and again, that's a very, very big if, you're going to need a complete washout tomorrow, complete, aggressive, really, really big amount. I'm out of the market. Forget about the market. This market's the worst, right? That's the feel, right? I don't want to use the word capitulation because you can't be in a bull market and be in capitulation, but you want to get people who bought stocks at really, really random prices and got caught really, really off-centered, right? With their pants below the ankles, those are the ones you want them to kind of quit and say, I'm done with the day.  Let me sit on the sidelines. Cash is a position. That's what we're looking at tomorrow. But if we do gap up tomorrow and we start rolling over, right? Get rejected of 60 minutes supply. Start rolling over. And again, guys, you can go literally chart by chart. It doesn't make a difference. If the market does have a day to sell off tomorrow, it's not going to make a difference. If one goes down, they all go down, right? So Amazon looks terrible. Netflix looks terrible. Facebook, right? Facebook looks terrible. Rivian looks like it really wants to test its IPO lows, right? That looks terrible. There's literally wind on the casino space, first close today, below this whole range here. That looks terrible. We're talking about Intuit. Look at Intuit. Right? Look at Intuit. Usually a name that I wouldn't look at, but again, look at this first close below this whole rising support. So there's a lot of value tomorrow on the short side. Again, you don't need to be too creative if we'd have another wave of selling. Just take your favorite stock. Make sure it takes out today's lows, right? Make sure it takes out today's lows. Let it put in the bottom, or excuse me, let it put in the low, right? Put in today's lows. Let it rally back, and that opening range low, if it takes out the new low, that's the guns blazing. That it will be another wave of selling, and this is where you can capture some pretty good alpha on the way down. So it's going to be a very, very important day tomorrow for the bulls. If you are a bull and you're looking for a reversal, you really need a gap down and then kind of wash red to green scenario. If you are a perma bear, you're praying to God for a gap up, stuffed into supply, 60 minutes supply, reversing course, going green to red, and start taking out today's range. That's it. Usually, I know it sounds funny. It says we're either going to go up or we're either going to go down. But yeah, but that's what the case is, and it all depends which way we're going to open up tomorrow. If the futures are good tomorrow, it's a sell bias. If the futures are bad tomorrow, we're either watching opening range lows or reversal back to the upside, red to green for a dead cab out. So we'll see. We'll see. Sometimes you have a game plan that's one-sided and you want to see everything confirmed. Tomorrow, you're literally seeing a possibility on both sides of the market kind of wanting and maybe getting what they want. So let's talk about today. You had some really, as you can imagine, some really aggressive selling today. Again, we talked about last night how technology just wasn't in bloom. We were talking about the caterpillars of the world and stuff like that. But there wasn't a case to be made about how, quote, unquote, strong. There was no strength in technology based on last night's bounce off the 50-day moving average. So these were the big levels on Amazon. The most important part of Amazon, you can see the 3320s, 3312s. This was 3302, excuse me, I'm dyslexic sometimes. Amazon's putting in its lowest close in this whole formation. This is the lowest close in this whole formation here. The last piece of area you have is roughly around the 3270s. If Amazon starts, again, if Amazon gaps up tomorrow and starts putting in, taking out today's channels on the low side, there's a lot of room down. There's definitely a lot of room down, especially if we have another wave of selling that looks really, really good. Amazon got hit pretty hard here towards the end of the day. Caterpillar 219 needs to build. Ironically, caterpillar, if you talk about strength in the market, that's where the strength of the market was today. Caterpillar got above the 219 level and went all the way up to 223. Congratulations.  Citrix got nowhere near $100. And then they started coming for NVIDIA. They started coming for NVIDIA, especially in the afternoon, very, very aggressively. First they came out off that 287 level, got it down to 285 and changed, snapped it back, but the key was here, that 283 level, that was yesterday's low, if it confirms you can see 278. NVIDIA got absolutely smoked really, really hard. It took out this 283 level, I thought it was going to stop at 278, went all the way down to 275. And now this whole bottom range here isn't playing for tomorrow, as you can see here. How many times it held this bottom range. So a huge move down on NVIDIA. The initial game plan today on Tesla was, if there is a week open today, a wash into the five-day moving average for a bounce back, that five-day wash was like after the world was imploding after the Fed, that was zero interest, at least for me. I was too scared to take any bounce on this thing. The worst part of it is I didn't even take the upside move in Tesla. There was a pivot here, 1156, I didn't even take it. I just wanted no part of the upside. It went up like $10, $11 before a massive, massive reversal in Tesla. Adobe got destroyed right from the word go, 538 if it builds below, it can flush. Look at Adobe, got massacred, absolutely massacred today. Got downgraded, traded all the way down to 514, Caterpillar, blah, blah, blah, take on the way up. Beyond was great. Beyond was actually pretty good. I just wish I had more liquidity. This is now an active swing. Last night we talked about they announced a deal with KFC to put their meatless chicken in Kentucky Fried Chicken. Correct me if I'm wrong.   You're not looking for no healthy chicken. The whole PR didn't make sense to me. Anyway, this was definitely the move, one of the bigger moves, 63, 60, if it builds below shots to go red. Again, this is an active swing, guys. There is no reason to be buying this stock. Everybody buys a stock now. I just don't get it. Anyway, it took out the 63, 60, closed right at the lows in 58s.  I just don't see a reason why this thing should be bought. The PR got sold off very, very quickly. 63, 60s got sold, confirmed it's 63. It sat there for like an hour and then finally just absolutely collapsed. Again, everybody, everybody.  Not hate Facebook, but I dislike it. Initially, I took a short of this thing. It goes down like a dollar in change and then some news that comes out. Some news comes out. I covered something into a wash. Some news comes out. It stops me out, break even on the balance. It runs up $2 and some fake news, yada, yada, yada. You turn around and it loses the 200-day moving average again. I looked at the close. This thing is down 7 from the 200-day moving average. Anyway, it is what it is. Qualcomm, not a big move, ran up about $1 off at all-time highs. As you can imagine, everything got sold off after that as well.  Anyway, here's my comments. Here's comments on Beyond get down to like 30% to 50%. This is at 61. Now it's at 58. Everybody should be down to like 10%, 15% on their runners. So a really good move there. The video is getting slammed next week's puts coming in for the 114, 270s, 79.50 next stop. It traded down all the way down to 75. Got absolutely manslaughtered. And that's it. And that's it. So going into tomorrow, again, if you're a brand new trader, it might be challenging. Okay, it might be challenging. There may be a lot of whipsaws. If you are fairly new to training, you might want to sit out the first half hour. Okay, let the market kind of develop, you know, develop some sort of personality. If there is going to be a DebtCat rally tomorrow, you're going to see it, right? You're going to see it, especially after a wash. If there is going to be another wave of selling, you're going to see that as well. So if you are brand new to trading, again, sometimes it's good to kind of digest, take a step back and just kind of appreciate the moment, kind of appreciate what's going on in front of you. So next time around, you're mentally prepared for it. Other than that, for all you guys who are experienced, should be a pretty good day. Should be a pretty good day. Let's see what happens exactly. Worst case scenario, we'll see if there's a theme develops after 10 o'clock, but most important part is let the trades come to you. Guys, have a great night, everybody. God bless, and I will see you all tomorrow. Take care.