Complex number || 11th Math || Chapter 1 Lecture 3 #complexnumbersclass11 @a2zpractical991

Which is our third property, what do they do if z equals, We take the bar over minus z, then what The part that remains after a complex number is divided, a complex number's I need to write formally: What is a complex number a superset of? Inside it, there are two subsets: the Real Subset and the Imaginary Subset. Hello friends, how are you all? I hope you're all doing great, having a blast, My name is Rahul Singh, we have done Mathematics Part 2 I had started the first chapter on Complex Numbers, which was from Class 11. In the previous lecture, we covered some aspects of complex numbers. We had already made some adjustments based on PropTiz's bases; what will we do today as well? This is our third lecture; today in this lecture, we will cover some We will read the propositions, and we will do some sums related to the propositions. Alright, then, without further delay, let's get going. Those that are even, we'll solve in this lecture, what does this Properties say? I will tell you about the power of Property Tax, the bar of Gare Property Tax, and what the bar of Mankeya Z is. You need to change the sign of it. What is the property of the conjugate of a complex number? It's the property of the conjugate of a complex number. So, what is conjugate? Before understanding what conjugate is, let's first understand what a complex number is. I've explained this to you all. So it was stated that complex numbers and numbers exist. Real number in Jaaf And imaginary numbers combine in the complex plane. And then, the number comment says the number. Khopaleksha number whose general form is A plus iB What is this? This is the general form of a complex number. Kavat Prex Naumar's soul has been devoured, this plus I B—if I extract its conjugate, what will happen? I'll tell you what to do whenever you take the conjugate of any complex number. So you need to pay attention to what an imaginary number is. Just change the sign of the imaginary number, whatever it may be. If it's plus, then subtract; if it's minus, then add. That's all we need to keep in mind. So, if I conjugate this, what will come out? What will the bar over z become, a What is its imaginary part? It is B. So, the sign of B is plus. So, add it, subtract it So this will become, minus b And it will remain as it is So, the conjugate of a complex number is just that number Whenever we deal with complex numbers We change the sign of the imaginary part. If it's plus, we'll subtract it. If it's minus, we'll add plus, so this one here Numbers are called the conjugate of a complex number Alright, if when Never let anyone ask you about the conjugation of What is the complex number plus IB? So you can say it's a-ib. Alright, so this conjugate And the properties of complex numbers are Understanding those properties, that's what we call properties. What do you want? Okay. So first, look at the first property, what is it? z bar ke If we do it again above, then What will come, z will come, then I will be here I'm explaining, what should I say Wants, what is Bar over z What does "bar z" mean? Then, on top of this, a bar If we do it, then z will be obtained Come on, let's move on from this Understand what this properties says Look, we know that complex number What happens is, z equals a Plus, I also exist And I have already told you in the previous lecture. when ever a complex number What should we pay attention to if we had to find the conjugate? the imaginary part that exists What do we need to do with his signature? Switch it; if it's plus, make it minus. If it's negative, you have to add a positive, right? So whenever What is the Z bar to him? A minus iB, and I'm also finding its conjugate So what the hell is it when ever We find the conjugate of a complex number So let's see, these complex numbers here its imaginary part of What needs to be done with the sign? When the real part of z is zero, z is purely real. They understand these properties And then we will come back and read these things again. Then you will clearly understand the things and the good ones. So we're off to tour our properties. Real number that is purely real If he is not associated with E There is no I multiplication with A. So, this layer here—what is it, your real part? And the number associated with I This part of yours, or what is known as the meniscus part, is exactly colorful. So what does it say when we people set Z equal, then we equate the conjugate of the gate to a busbar equal? So the one that should be Z should be a purely real number. By meditating, I understand this property—I'm roughing it out. I have already mentioned in the previous several lectures that Z equals A. Plus, I am also there, where there is one or your real part, and the one I too have a part of you, what's your imaginary part, okay, this thing here I've already told you, we accept that LATE Z equals What would happen if I took the conjugate of this? Okay, and what is Borra that Z equals Z Marshall? If the conjugate of z equals z itself, then what will be the result? The one you have here will be the real part of your cooler. What I want to say to Dihana is two words. If z is a single tool I will do it myself. So what is the value of z? A Tlas I B is. So I'll write A, T, L, A, S, I, B for this. And whatever your z-bar is So whenever you have z, which is your complex number, if its conjugate is equal to the other one The number that should remain should be only and only a real number. The real part should be purely real. Here too, a is the real part, and here too, a is the real part. I hope you understand what I'm trying to say. Look, if a plus i b is Can they be equal to a minus i b? They cannot be equal, right? So here, the point is that the value of b will be zero here.kbd搬家 If the value of b is zero, then a will be equal to a. So, this number, which is the conjugate of z, is a purely real number. Is there any complex number associated with this? Is it in the form of Form ITR-1? In the form of the real part So what does this property do, whenever z equals z? Alright, z equals z, the ganga gate is equal to each other What is there at that place where z is? What else is there, if not yours? that a purely real number is I hope you have also understood this property. We head toward our third property. Which is the same property I just mentioned to you It's exactly like the property I told you about. I hope you have understood these things. We walk toward our next properties. Which is our third property What do they say if z equals We take the bar of minus z. Then, the part of the complex number that remains What is a complex number? real part and imaginary part So the part of the complex number that remains after cancellation So this is plus B. This is a plus sign, it's B. What do you mean by "real part"? And B, we're looking at you. imaginary part So, AM people speak purely real numbers. And the number that comes along with it We call it a purely imaginary number. What is it? You already know these things, I've already told you in my previous letter. What do you call this? I don't know, but I'll give it to you for real. Pull real, this one. It is a real number. We call this a purely imaginary number. Kewal B. Ko is a purely imaginary number We keep walking. toward the third properties to understand What is Kaushis trying to convey about the properties? toward the properties which are the third properties z equals It's z bar. I keep on doing it, even if I shouldn't. What is that thing over there? What will come if I extract Z bar from this? A minus iB will come, right? And Whose equation is this? Not minus, not this Z bar minus I'll multiply it on both sides, so this will become minus A, that's your answer. So I can only lick one spot at a time, what is this anyway? Zero Wey H Zero, okay, on the same spot, you zero rock two So what will 0 plus i be equal to? Minus 0 plus I B and zero, what could it possibly be? So, what we get is just the imaginary part. Whenever you take the Z component, you subtract its conjugate, and then you multiply by the imaginary unit, you're left with only and solely the purely imaginary part. If you take the complex conjugate of I B and then multiply it by I B alone, you are left only with the purely imaginary part. If you take the complex conjugate of just the imaginary part, and then multiply it by itself, you are left only with the purely imaginary part. We will walk through it, making it our problem, and there lies the strength—first, I present the problem. So, I have stated the first problem: 1 plus 2i minus 2 plus i. Okay, this is our problem. I am growing with your problem. So what can I do? This is a one, isn't it? Can I multiply one? With which term can I multiply minus 2 plus i and plus 2i? I can do all these things with minus 2 plus i, which you all studied in class 6, 7 Therefore, I am not trying to explain by forcibly connecting these things together. Why, because you're probably coming along very well You are in Class Two Eleven today, correct? So, Job, you really ought to come here. This is your minimum requirement. When the heir is coming, you must bring the things marked. What can I do now? What will happen if this is rooted at 1 and 2? The number 2 will come, and what will happen to the root at 1? One into I will become I will come. Plus I Because this is also plus, this is also plus. Plus into plus results in plus. So why is this happening? One ant will die if it is multiplied by one in this. Vaccinated, written down I Minus two Plus Okay I Minus Furai Okay What is the value of I scare? What is the value of I Scare? It is minus one. Dago, Power of IOTA, I'm here for you all But in the purse lecture, I've already told you—I'll write something down for you. Please keep those things saved in your mind, and based on that foundation, we'll solve some problems. This bus, what should you do, remember this, remember, it won't be remembered This bus was here, this bus will be remembered Keep this in mind Look carefully, what can I write? Look carefully, this one times this one did it 2i, 2i multiplied together equals 4i². Then 2i scored, okay And in its place, what can I write? So 2I Square was there, so what could I write about II's place? Can you write Mansa Forest? So here you can write minus two Right on What will happen? It will be a jungle, won't it? I'll write it down as you said. What kind of pain is this, and what is the remedy? Four people came, two people, two minds, what will happen? Nine people will be there, Araya, and four people will come. What is the meaning of the word "Khan" that has come to be used as a title for a man? So here I can write minus three I Right on So, this is your answered first question. Which is Minus first plus three i has come But what are we supposed to remove? Look carefully I mean the one who gave the gift Write it first in the form of A plus I B. Then, calculate the values of A and B from there. So what do we have to do? We need this minus first Compare minus three i It is necessary to compare. With whom They are walking with their own problems If you don't understand this, then So, carefully look at the next problem. And understanding, you bid, Herrn Tell me in what way I am solving it, that's fine, this comparison will come to you. No, I hope you understand now. I'm just clarifying what I've done with this. minus four minus Three I Equal to whom? a plus i b We have to compare our expression whether we wrote it in the form of a plus I B a plus ib What is it like in the form of a plus Ib? I can write it in this way minus four plus or minus three i I can write it in this form Whose form is this? It is in the form of a plus sign. where the value of a is minus four And what is the value of b? What is Aam? 1 And I write this here for I. Press minus three antenna, or this antenna press minus three. See this, this is the same as that. Look at Dihaan. I am here. Where A's Bhelu Madalu Manas 4 is located What is B's Bheelu? Manas 3 is it. So, thick plaster I will write it here A's Bheloo Manas is 4. B's Belu Ruru spoiled mind 3 is I will understand your intention when you come to Ho Ho Bo. So what is the problem: i plus one i minus one to the power minus one? Okay? What is my next problem? I plus one and 1 minus i i times one plus i times one minus i to the power of i, okay? Sorry. Proberm Thabang Khala What's written in my problem? Inside your heart, a parrot has taken residence. Bolories, here it is seen He kicked the ball. What does Subhane do? I don't know randomly, I'm not telling you the whole truth or just a part of it. The problem is exactly this. What can I write for this? I could write one upon a They are this kind of pioneer And what else can I write, I am one plus i, and this is my one minus i Exactly, whenever you have complex numbers, just express them in the form of complex numbers. If any numbers are visible, what should we do about it? Even this appears on the scale, what about the minus sign on the balance? Not Ah Phone Time can be scored, as the third one is not raised from Scor. Formula, keep in mind that whenever we have plus beer sina I'll write the holy square. So I can write it down One Plus I's hole square up on What is this? 1 minus i over 1 plus i What should I say to you people? Whenever the expression (a plus b) into (a minus b) appears in the formula I need to write a story. You must keep in mind the properties of the Power of IOTA. Plus i squared is minus one IQ is minus one I'd say it's four, so one You don't even need to bother memorizing this. You'll understand the necessity, how we can extract it without even remembering, right? If you even slightly apply common sense, you'll realize these things You can just extract the I call to root up minus one, keeping that in mind, right? What can I do with minus one times minus one plus one? Look, even if you see the forest minus one, it becomes zero. When zero arrives, I will be on its origin. For you, I give it. What will happen? Zero plus you came Upon What is one plus one? Two will come Here are two options for you. My zero Plus, you came out from your own place. Open What can I leak now that it has Babu of this I can write it like this, separating it in this way, or I can write it like this, separating it in this way—yes, I can do that, can't I? When I separated it, you started dividing from zero. If you divide zero by yourself, what do you get—zero or something else? And this will be canceled too. What should be done when the cancellation is confirmed? Zero plus I will come out. Alright And the number that came out for us Zero Plus I is in which form? In the form of a complex number When it is in the form of a complex number So we need to compare with a plus i b And provide the values of a and b So what can I do for you? i Compare with a plus i b What is the value of a? Here, the value of a is zero. What is the value of b? Our i is What is 1 divided by 1? If I am here, then there is one hidden here, so what is the value of B? The value came out to be one, and the value of A came out to be zero. What is the value of B that came out? One. I hope you have understood this problem very well. I solved it in this way. If multiplication arises, we must perform multiplication in the way we solve our problem, then apply it to complex numbers. It must be written in the form of 0 plus i, and then what needs to be done is to compare it with plus i as well as with one. I What does "Nahan se dekho, kya likha hai? I 4 plus tri I Okay, aapka I hai koi plus tri I aur ya aapka A one minus I Okay, maine Can you multiply this I by the bracket? What will these become for us? 4 i Plus 3 i Square Right Apon 1 minus i, so I will I'll write it as it is. Right on Look at it with your eyes It can be placed on the minus side. Okay I hope you all can remember this so well You're already reaching class 11 You must surely remember this. Okay Look here You can keep the square root of v minus r. So, what will they do for Legas Daily? I didn't feel anything wrong at all. Because it's empty, as any section would have gone anyway For this, I said, "Come on, let's go." The other section also gets as many people. Because or not, I don't know why Will minus three come? What is this, anyway? I'm telling you all this, look, one minus i that whenever we have our denominator If things appear in the form of a complex number Plus i here my Ford a minus three, this one plus i, okay? Look, one minus i, Nikki, said this What should one do when Apnose B appears in the palm? a squared minus b squared So I directly do a² - b² on this. If I do A2, what will happen? 12 Minus What is B2? I2 This will become your i2. Alright Now carefully look What do we have to do? This 4i Multiply it with this. And minus 3 as well So I'm writing here What am I doing, Dogo? Whatever i2 is here I value him whenever he wakes up. Look carefully What is it? 4I Plus 4i2 is there So, what should we write instead of i2? Write minus 1 What exactly do you need to do with this? From the Plus IB's Forum And one's value at the place of honor And the value of B at that point Write it down And this is ours -7/2 Plus 1 by 2 Compare this with how. A plus I have to file the IBE form. When you have this -7/2 plus i-storage 1/2 Equal to you, I will compete with Aa Flas Bee. Then one value will give you minus 7 by 2 Carpe velu canonical will arrive, what is the value of the du by key? Kani will come tomorrow, one bat, luck came to you Explain how I approached this problem Soul has been contacted, that's all you need to know about this tape. Keep going, keep striving, and thus keep moving forward So our previous information is Class Eight, Ninth, Tenth Sometimes we have A plus B, A minus B When the form arrives, we need to calculate a square minus b square. Properties like these, peak peak properties, and Something about this wandering spirit I am doing it, and I can do it. What is it? Injury What is 2 plus i over 3? 2 plus i 3 minus i What is our 4th problem? 2 plus i over 3 minus i, look closely What is 1 plus 2i? 1 plus 2i, that's it And let's go solve this problem carefully—look closely. Then again, if you haven't understood, look at this problem. And try to understand How exactly should I follow the step? And I'll solve this problem, okay? Look, what can I do? What's this? You've given 2 plus i. 3 minus i 1 plus 2i is given Whenever I leave 2 plus i in agt, I don't make any changes. What can I do, multiply 3 with this bracket And I can multiply minus i with this bracket. So 3, 1 plus 2i Right, minus i I can write it like this: 1 + 2i And what can I do, this that belongs to you Right there, 2 plus i, what can I do with this? Stay, 3 multiplied by 3 won't become 3, it'll be 9. When we don't add 3 plus 6, we won't get the result. And they will not make a false move. Here, what on earth will come if Ayi comes to Ayi? them, between, and Because you have reached class eleven, and all these things will be very basic for you. Even so, I'm telling you something very basic, okay? But what should I tell you all? Wherever the score appears, I need to write minus one. So what do I do? Just look carefully—this two plus i, right? It's here. So what do I do here? I can take the common factor of i from both terms. If I factor out i, I get 1 plus i. I get 1 plus i, i, and then I take something like this. When we have the denominator, it's complex. Alright, I'll write this down, and then what about you, Kana? Do you have this? To conjugate and rationalize So what will happen to this? Conjugate 1-i 2 on 1 Manos, I do it this way There, Shabir is a great fool. What is it? If Garoo is shouting loudly, then the others are also shouting. This is Bharat. Sukri's river has been seen by Garuda. No, it does not fall from India. You want to do it this way too; you can do it this way as well. But I will tell you people Because these two, A plus B, into Amanis B. It's becoming a formula, so let's consider it as Square Man. We write it in the form of B score. So I will do this here What do I do? I am a forest scout, I am a human scout. It will be easy for me. You also must do it in this way. Why do we need so much It's complicated, but I'll handle it. So what should I write in place of this? Five of them scored Look, these apples are made of B, the foam of B. So we don't know What should I do? I need to make a hot mental map. If number A plus B into A minus B is appearing in the form I wrote down these things using exactly those formulas. Now, what can I do? Just look at Dihana. I hope you can see what I am doing. I can be real, and I can also multiply by plus I. If I can afford it with I, I would do that. What can I do with these 2 multiplied by 1-I? I also write it on the next page. I hope because this thing won't be visible to you If I solve this I'll write it on the next page, okay? First, let me write down what our exit is. 2 plus i 1 - i What's coming out? 2 plus i 1 - i And what is coming out here with us? File 1 square Minus i squared It was our turn to leave. Alright We'll solve this again from here. What did I say that we have to do? Multiply by 2, this bracket together with 1 minus i And this plus i multiplied by upon File What will come for 1? If I square 1, what will come out? 1 will come out, and I will square i So, what do you say? Minus 1 will come, that is, this became your 1. Instead of minus i squared, I have minus 1 I can write, that's fine What will I get if I combine 2 into 1? 2 will come, and 2 into What will come out if I |_|? Minus 2i will come out, okay What will be the result of plus i into 1? I will come, then here it will be I write i, and this i of Apon Look through meditation: what will be the value of Phi one plus one? Two So, how much will five into two be? Ten will be. So I'll directly write ten here. Alright I hope you will explain to me what I have done so far How much was it if Mahin comes today? What is the symbol for the largest number? It's minus, isn't it? What is the sign? It is minus. So what can we write in place of this? How much will Jagpe Two One be? If you're tired, then you're tired of these... You run this way, you're worthy They used to run away from the scorching heat of the sun. Here I write I What form is this? Which form is this? It's a complex name, isn't it? Then What do we have to do and compare by doing and making? You need to write your value and also the value, okay? So what do I write: 3 by 10 minus i What is this Acul Tü? App Player I'm B What is the value obtained from one? 3 by 10 and What B value has come out for us Minus 1 by 10 I hope you will forgive me What can I write for this 3 by 10? I write it in this way 3 by 10 Then what should I write for it? Plus Minus 1 by 10 I This form can be taken, and what is this? This is in our A plus B I form, right? So, what is the value of B here? Minus ten, so here I am, minus ten. I am Daret Lika vaccine Here, I have told you the method by which it was extracted. Okay, so what value of B have we arrived at? It has been found that B equals minus 1 over 10. Alright, I hope I sweeten it for you. You must be confused. There will be confusion. Just one minute. I hope you will explain to me how I solved this problem. Right, what do you all have to do? Whoever is having problems with this method We have to keep solving it step by step from here. And the previous information we have for classes 8, 9, and 10 If there is a formula based on that information So the formula we need to remember is this one And using this formula, we can easily solve the steps for this. Alright, let's move on to our next problem. What was the next problem? I've already told you this, right? Let's move on to our 5th problem. We will solve the 5th problem. And what do you people have to do? Alright And I will check that problem there for you. I'll check whether your result is really correct That is wrong. I'll let you all know by commenting Whether you have solved it correctly or not Alright, then let's solve it. Your 5th problem What is the 5th problem? No a b ka janchan tan tan tan ka formula kya hai If you are a small child, then I have written it down for you. What do we need to simplify? So, what will one square be? One Plus, I'm writing directly. two into a b two into one What will happen to y? Two y's will come. All right, and what else is there? Our B I Square is fine. So, if I square i, what is the value of i squared? minus one, so I'm here at Next step, I'll take his place I will write minus one, then again a Apply the formula for the square of minus b and then If you want to simplify, this will become one square. Here, minus two y will come. Plus, what's going to happen here? I will come square, it's correct, right? And what should we do in the next step? It will come. One plus two y I am you guys What is the square of i? Show it to me in its place. Do we need to write minus one? Alright, so what should I write for its title? I am Tika, this is minus one on one minus two I To write What should I do? No longer comes It is a scientific name. Why are you looking? What is it? Not connected What happens Why do it? No Why is it needed Why? Is being done A long bus Full turn What will happen? It will be canceled. So, will this also come our way today? It will come today And will remain here minus 2i This is where you'll survive. And I can cancel these two 2i terms. And what will remain here? minus One will survive One remains minus one. What should I do with this now? Write the complex number on the quaternion. What is a complex number a superset of? Inside Jiji's What is a subset? What is the real subset and Imajiredi subset Every real number is a complex number. And every single emergency number as well What happens A complex number is So how do I express minus one in the form of a complex number? Look, it's there Let me tell you, it's the Mi Note 10 Pro GT Edition. Either say GTI first, or I-one said GT. If it proceeds, I will write it in the same general form as our complex number. Right on So what can I write for this, minus one What can I write? minus one plus i into zero And then, comparing it with the general form of a complex number I can find the values of a and b, right? a Plus IB Compare with This is minus one Plus a plus I am zero. Here This is ours equal to minus one Him Louiou Kaki Deba Nore me ne feed Raneje lanreyi 2nNIS adite syalch bayant medicine pala ench palukent bhayey We will take the Barrie Portlum to the Next Lecture Show. You all go and show the power of Karfa to this Porlam. And see whether you can handle this porlum or not. And if you get the solution, please go to the comment section and let us know. That my solutions have arrived I'll send you there Like or unlike, or feed or unfollow, you all I will tell you whether your problem is correct or incorrect. Right on You write the answer, and I'll check it out there. Thank you, I hope you have a great day today. See you in our next lecture. Thank you until then.