Complex Number 11th Math || Chapter 1 || part 7 #complexnumbers @a2zpractical991

Piyab Chala Tad Yavundhi Yhanati Tanme Pate Chad Yunted Dotrdend Milega Uth Tadoend It's the same one, the one that's for one-on-one, the one that's for one-on-one. So let's go without wasting time. You've prepared the lecture, so let's quickly go over what kind of problems we need to solve today. So, you're showing everyone that here A equals What is written in A? Negative one plus the square root of three i over two What is written in B equal to? -1 - (√3 i)/2 Right on What proof do we need to provide? if we square A Then the value we will receive Right on So, you see What should I do? I only have A square equal to B I'll prove it to you. And next task I will give to you all What do you have to do? By squaring B, you get the value of A Bring it back after taking it out, okay? So, tell me, what needs to be done? To make a square What else can I do? To make a square A square here will be done. What do you need to do? As I didn't do This is just a rule. But stay focused on your work. It's the child's turn Look, look, here there is a two minus one value So, plus into minus will become? Minus. Look, I'm writing Daret Then this is the forest, Into One and B What is B? Root of three i Alright, this is it and What will you get, and what else will you get? I will get it in the square. And in the previous lecture, I showed you all Related to I-key, related to I-key power Keep some values, what is this? If I equals what? Root is minus one, okay? What will I get if I equal to you? I'll get it squared away, I'll do something about it What's the value of i squared, minus i? I come, and even more, I am the bond of the river's flow. So, from this square, we get value one, okay? minus one If I change plus to minus, what will I get? You'll get minus; just watch me do it. You can do the same thing to me in the next step. plus becomes minus will be combined And if I multiply three by one, I'll get three. Alright, so I need to rough this out Alright, what am I doing with this? So, if you add and subtract, what will you get? It will become minus 2. Because the larger number is What is his sign? It's negative, okay So this is minus 2, minus 2 sqrt(3)i What did you get, 4 This is the verified date Have you proved it already, we people That is a 2 Who is older than whom? B is older than K, that's correct. A is on top of B, and B is on top of C. That's exactly what I wanted to prove, correct? The way in which I proved a² equals b What do you people need to do then? The way I used that methodology You must keep solving it. We need to find and show b² equal to a, okay? So I hope you all will solve this problem yourselves. Alright So let's move on to our next problem and take a look. What is our next problem? Look, the next problem given to us is this And we need to solve this problem, okay? So you will have been studying from class 8 onwards The formula for (a + b) to the power of q So some formulas that you people have been studying since class 7, 8 If you do BSc, you'll get messages, wherever you go You people, this formula won't leave you alone, that's correct. So, all these formulas should be remembered by you all, okay? As long as you people think that mathematics is a part of our life By then, you all should definitely remember this basic formula. So, tell me, what is the formula for (a plus b) whole q? I'll write down what's here a^3 + 3a^2b + 3ab^2 + b^3 You should remember this formula. If you remember this formula, you will be able to solve this problem. Alright, let's go ahead and solve this problem, and see the approach I'm using to solve it. Alright, if you guys are happy, then you can solve this problem, so here's the video. Quarsh karo aur sol karo aur dekho ki aapka result kya nikal kar aata Match it with my result, okay? What is the value of x plus i y? What is equal to a plus I B ka Whole Q Thike So x plus i y equal to a plus i b whole q, so given A Q, A Q, what is here, A is here, so A Q Abe, you're staying here again, plus 3 a squad I don't want you to change anything about this. Look carefully here, what can I write? 3 a square b I can write Okay, and what can I write for this, IQ Then how can I possibly get to BQ? Look right there, you. A plus What is equality? One plus Three a scout I B Thake Now what should I write to IB? I'll write B first, and I'll write I in the middle. Because it will look good That's why I'm doing it; even if left like this No spark is struck. So what do I do? I just give up. Now it's okay Write something Do whatever you can to simplify it as much as possible. Simplify it, okay a q Plus the AI scored BI Right, and look, plus into minus what plus What will happen if you enter here? When 3AB comes, what should I write in its place? 3AB Okay Plus into minus, you will do minus and Will IBQ come? Will it come? IBQ is coming soon. What should you people do now? I need to write the real part and the imaginary part together, is that correct? X plus I said the real part and the imaginary part. Write separately if real part Yes, together with the imaginary part and the other part together I don't see anyone else with AQ. What should I write? 3AQ-3AB Alright Write them together Then what do you people need to do? To be compared What you write, comparing the real and imaginary parts, fits each other Write it fully, fit it or adjust it on its place With Aekas You, with great concentration, this problem What is written on the two stones, X by A and Y by B, of these two? If you calculate it, I want this result to come out for you. So, what is our main focus? To remove X by a means x by a by b to subtract with the help of this x by a and y by b to subtract What can I do? I can take a common if I take a common Then what will happen a square minus from here a common What will be left 3 b squared OK and this multiply If I take this side Then it will go to division. this x by a and what will happen a square minus 3 b squared OK likewise from here why by from here What can I do? I can take a common OK so when you take a common then what will remain 3 square minus b squared OK and from here Multiply by b If I take this side Then what will happen It will go to division. OK so instead of this What will you write? 3 square minus b squared OK I hope you understand. What I am doing OK Now what do we have to do? What do we have to do? We have to sum x by a and y by b and we should get this value OK So what am I writing left side x by a plus by b We have to do this. and our result which is our desired result Let's see. Let's solve this. Let's see. what we get the value of x by a What is it? a square minus 3 b squared OK and the value of y by b What is it? 3 square and minus What is it? minus b squared OK and see a square and 3 a square when you add what will you get 4 a square what will you get instead of this What will you write? 4 a square and minus 3 b and minus b squared what will you get minus 4b squared OK Now what you have to do Take 4 common what will you get you will receive a square minus b squared OK x by a and y by b when we did when we sum what we got answer 4 in parentheses a square minus b squared We got this. OK So we have to prove this. I hope you understood. this problem OK We will move. to our next problem and We will understand. how to solve See if you solve more problems then your mathematical aptitude will develop so after some time you will feel that I will be able this type of problem by myself There you go. will not need any teacher OK so for that You have to solve more problems OK so Let's move. to our next problem and I will solve this problem See if you want to Solve this. problem then first try then post it and your result will match with my result OK so we have to this problem and See you can write a square d square so I will write a square d square equal to c square plus d square whole square OK now what I have to do is I have to write a d square equal to c square plus d square OK so I have to square d square equal to c square plus d square whole square OK I have to square plus d square equal to c square plus d square whole square OK so I have to d square equal to square plus d square whole square OK so I have to square to d square whole square plus have to write a d square equal to c It will become very old, okay So let's move on to our next problem and take a look. What is our next sum, okay? So our next problem is 21 We need to solve this problem. Alright, so what's the problem given? Look carefully, what is written here a plus i b equals 1 plus i, 1 minus i What is written, a plus i b Alright, equal to Given, 1 plus i upon 1 minus i It's written down, look here I will provide a rationalization. 1 plus i Look, I'm writing this directly here, okay? What should I do, me Right here, direct rationalization I'll take it, look at this Writing in this way, but Above Taus, multiply below. 1 Please I, and 1 Please, I need you to do this, okay So what has happened, 1 please I Into 1 plus I became, 1 plus I's Whole squared, sir, your a square, a square minus b square The formula will be applied, this will become I squared, right? And you all know what replaces I square? Can you write? If you can write minus one, then show me. I am looking carefully here, writing this down, one plus I squared, one minus minus one Will it become minus into minus? Plus will become 1 plus i squared What could it be? It could be 2. Minus times minus becomes plus one. Plus 1 will be, 2 will be, okay You've come this far, don't betray yourself here either And for the Jagbhai of I Square, you people will write minus one. So, what will come in plus-minus? Minus will come. It will be minus one for you all. What is it? It will come to you. Okay? Will the answer come out clearly? From the body, the plus What will one minus one be? It will become zero. So what will remain? To I, my to Where Two Two was canceled So, what's left of you all? Apple I be equal to you, I be a child So how can I write this? And you people need to compete with whom? real and imaginary With part So what value will you people get? Zero. What value will B get for you all? A forest will be given. And what exactly do we need to do? How much should a single two be worth? Forest Plus One What will be given? Forest They are together They are equal, right and left hands, what happened? Hans Propp, you can write below this a squared plus b squared equals two one, okay I'll explain the problem to you all; it was a very simple one, okay? Alright, you guys take the scale shot, I'm the side art. I will make you a good friend after this. This is our next problem; we need to solve it. Look carefully, in what way can we solve this problem? This is a very simple problem. Look, I'm giving you this problem first Or else I'll tell you directly Look, 7 plus i root of 3 What is written here, 7 minus What do we have to do, carefully What we need to do here is quite unique. Look, it's really quite different. However we may, we must create such a unique and grand thing. It's similar, but I I saw that, I I'm here, I was direct here Then, when you perform cross multiplication, 7 plus i times the square root of 3 square root of 7 plus i times square root of 3 What is this? It's the same. Then it will become the whole square. 7 plus i root 3 The entire square has become So both are the same. It's the same as both are similar. What will happen to each other? It will become a complete square. square root of 7 minus square root of 3 What will happen to this? It will become a complete square. Plus 7 minus square root of 3 This formula is being formed. So, what exactly can you write directly for this? We can write the square of the square root of 7. What else can be written? minus i root of 3 entire square I hope you all understood the things. What do we have to do? We need to perform Crosh multiplication. So when you see root of 7 minus i root of 3 These two are the same. So when these two are the same Then, when you multiply these two, What will this become? (a + b) squared will be formed The square root of 7 - i And when you make its denominator the same What is this becoming if it's a thorn? (a + b), (a - b) whole squared The formula for a plus b, a minus b What we people write in the form of a square minus b square It is a thorn. So I've simplified this from it What is our next step now? We need to simplify this. If it's a square of (a plus b), then use the formula for the square of (a + b). When you square root 7, What will be given? 7 will be given. 2 times root 7 into root of 3, I yeh It is a thorn. Then plus What do you write this as? The square of the square root of 3 It is a thorn. Then look at this What about this one too? The formula for (a - b) squared is: (a - b)² = a² - 2ab + b² What? 7 It's a tick, you can write it. And what can you do about it? The square of the sum of i and the square root of 3 It's time, I hope you all are Things should be becoming clear by now. And what is below, both of you? Square the whole of root 7. When you square the number of the root So, the full number comes in place of it. What will come? 7 will come. minus i squared 3 will come, it's a trick And what value would you assign to i squared? If you put minus 1, what will minus into minus become? What will happen to you people if it gets added? What do you two have to do with us? You need to simplify this. 2√7 × √3i -2√7 × 3i Plus Eve both with each other It can be canceled, it's true. And what will 7 7 be? It will be 14, won't it, 14? Then I'll write 14 in its place, okay? And what could this write? What will this become? I square into 3 So what will this become? 3i squared So I'm writing this directly: 3i squared makes OK? Who else? 7 7 So we'll make it 14, the kid's still here What will this become for you people? 3i squared will become, correct? And what is this for you people? You all's 14 You must be squaring i. What is the value of i squared? Minus one, then plus minus what will it be? Minus 3, right? What will come for you guys? Minus 3, will this also come? What will happen if you subtract 3? 10, okay? 14 OK? How can this be written? From 14, I went to 6, what will remain? OK? So, 8 will come, 8, 6, making 14, right? Your 10 What do you all need to do now? It needs to be divided, 24 go 8, 24 January 10 What exactly will come? 4 by 5, correct? So, what's the result of 4 by 5? So when you simplify this problem So you'll get 4 by 5 And what is 4 by 5? What is 4 by 5? real number Okay? So 4 my 5 what is it? real number So, this is what I'm showing you all. You have to write it below. square root of 7 plus i times square root of 3 over Whatever is written here is a real number. Write it down here, you people. Alright, I hope you'll explain things to the people. Let's move on to our next problem. And let's see what our next problem is And in what way can it be solved from it? So, looking ahead to our next problem, let's see how we can approach this problem How can we solve it properly? So what do we have to do? What have we been given? The cube of x plus i y is given, correct? Do you know the formula for the cube of (a plus b), yoga? We just need to use that formula. The whole square of i y is located here 3 times square is correct And what is this, wake up? The cube of i y is correct. What else is there? y plus v i correct What do we have to do? We need to simplify this. I'm just simplifying this. x cubed plus 3x squared and I to you I I'm writing it on this side. Multiply i by x or multiply y by i It doesn't matter, alright What is here? 3 x Look, the square of i y is damn awesome x squared plus y squared will be correct Then what is this, awake, i cube It will be y cubed, right? And then what? y plus v i is What do we have to do? We need to simplify this even further. So what is x cubed? plus 3 x squared Now, what should I write instead of i squared? Monos nice y squared will be in place of i cubed y plus v i will be What do I need to do with the real part and imaginary part? Write them separately, one after the other. So, write down all the real parts together. xq What else is there? Minus 3xy square What do we have? It is the real part. Write them together Alright And then what? It is minus. Alright What is plus what? This is not a dog. Image not part y Minus i cubed Can I write it this way, can't I? Pi R squared plus V I Now what we have to do is compare. Real part and imaginary part, please write them down. What will you write, you people, comparing You need to write this down, okay? After that, whatever is given, separate the real part and the imaginary part. Write them together, the real part of this x cubed minus three x y Square, okay, what is this equal to? You, the one who has given me this later on Free X after minus Y cube What is this equal to? V is equal to. Okay. What on earth is this X Y thing? Take x from here. So, if we can take it out, what will this become? You people will become x screecher Minus 3y will become a scrier, right? What is a single? If y is, then you can write x together with this here Okay? So we won't write the next step with him. 3xy Scrir Bchka y Scryer, the child OK? What is this? Dhi y by x This is what has become of you people 3x Screamer Men's y2 What on earth is this going to become? b by It will happen. Alright I hope you will explain these things to you people. equation One give it equation Two give it to me Alright What do we need now Prove it for us x by y Meaning x y divided by x What needs to be done? y by x plus b by y To calculate the sum And we need this answer Alright Pay close attention, you two What will you all do from here? Take it common Here, four will come in. So what will happen? x2 Māninas y2 It will become And this is exactly what we had to prove. Your x y Your x Pals Vee When you sum it up, this result should come out for you. Which has also come to us So, what would it mean if the left-hand side became equal to the right-hand side? So I can write from here what has the left-hand side become On the right side, please write it here. left-hand side equals right-hand side Therefore, hence proof dead And what can you write? What is y divided by x multiplied by v divided by y equal to? 4x squared minus y squared is equal to I hope you all have understood the things. Alright That's all for today See you in our next lecture's lecture. Thank you until then