5

Ine correct expression below.0+9)- FxThe ' real part of zz" @5 The imaginary part 0f zis : Zxy _4y2can be written in terms Of z andZ as ~(z - 2*)2i(zn+T)7...

Question

Ine correct expression below.0+9)- FxThe ' real part of zz" @5 The imaginary part 0f zis : Zxy _4y2can be written in terms Of z andZ as ~(z - 2*)2i(zn+T)7~l where n is an integer{z: Iz-i| = T} is circle centered at and of radius{z: |z| > 6} describes ihe interior of a circle of radius 6_Im z >0 represents the right portion of the complex z-plane4in6)6+0) = ~2ilim (22 + 2z + 5) = 1+4i 2-21

Ine correct expression below. 0+9)- Fx The ' real part of zz" @5 The imaginary part 0f zis : Zxy _ 4y2can be written in terms Of z andZ as ~(z - 2*)2 i(zn+T)7 ~l where n is an integer {z: Iz-i| = T} is circle centered at and of radius {z: |z| > 6} describes ihe interior of a circle of radius 6_ Im z >0 represents the right portion of the complex z-plane 4in6)6+0) = ~2i lim (22 + 2z + 5) = 1+4i 2-21



Answers

In Exercises $1-20$, find a polar representation for the complex number $z$ and then identify $\operatorname{Re}(z)$, $\operatorname{Im}(z),|z|, \arg (z)$ and $\operatorname{Arg}(z)$. $$ z=5+5 i \sqrt{3} $$

You know we happen to number five And this one to find various things regarding to this complex number. Is that equal to my six three plastics harder the first days the real part real part of several bay that without our design. Okay imaginary part of that will pay the term with uh I don't know and zet model s this is also recognized are is the real part of square players even the party square a little. Okay So 108 place 36. the route 12. So that mod RR is 12. Okay. Yeah, no we have to find the argument for that. We have ascertained the quadrant and the these points lay Points at -6 year old three And comma six so this must be in second quadrant if this is alpha this is theater so theater will be five minus then in verse we should say by minus alpha by minus can inverse imagery part barrier park without negative sign. Yeah 66 billion cancel out so by minus tenuous one by three minutes. Bye bye six so bye bye bye first. So this is the value of theta no argument will be equal to Fight by by six Bliss to occupy where okay belongs to the interiors. Okay and jesus principal argument will be the value of the argument which belonged to the interval minus pi to pie open at minus pi closure pie. Mhm So this will be argument of zen and you can always observe that only five by by six is the argument that belongs to this. Okay now Solar farm will be our 60 to So are is 12, 6, 5, 5 x six. Okay, So they should be the answer. Thank you so much. These are the answers. Thank you.

Okay, We have these two complex numbers given to us in polar form, and they want us to find Z one divided by Z to find that quotient. Uh, there's two things we have to do to do that in this form First is we have to take the radi i of those and divide those the same way They're divided here. So Z one take its radius divided by the radius of Z too. So that would give us 3/4 has the radius of our quotient. And then for the angles. We have to take the two angle measurements from those complex numbers and we have to subtract them again in the same order that we are dividing. So Zi Juan and numerator, its angle minus Z two angles. So pi over five minus pi over 10 is the direction we have to subtract and to subtract those we need a common denominator, which will be 10. So we just multiply the first traction by two. That gives us two pi over 10 minus one pie over 10 so that our angle expressions that are gonna be the cold sign off by over 10. Plus I time to sign of pi over 10

Hello, everyone. So here we have a question. Imaginary off 30 goes to negative five upon to. So this part represents the imaginary offset. Where? That is it. Complex number off the form A plus B, I Okay, so in this complex number, there is a real part which is this one and the imaginary parties. This one beat. So this equation given question our represents, actually b equals two minus five upon to now for, ah, the complex plane we can use B s y okay. In the complex plane. If we take X and y. So then be we also represents Why? So we can write why it goes to negative five upon to. So this is the, uh, equation for who's the graph has to be drawn. Okay, so let us draw a graph. So why Cause to negative five upon to? So let us draw a few points on the graph. So I will draw in the negative wakes is only because our point is negative. And why question Negative five upon to So this is negative. Half. This is negative one. This is negative. Three upon to this is negative two, and that is negative. 5.2. So our point is this one. Okay. Negative. Five upon to when? So we have to draw a line which is just passing through it and parallel to the x axis. Okay, fine. So this is the required, uh, graph off the equation. Imaginary is that it goes to minus five. Open toe. Okay, so I hope you have understood. That's all. Thank you.

We have our number 12 in this trying to find ah first things for this complex number that equal to I. Q. wrote of seven like this. So first of all a real part of that there is no term without I. A. to the real part of the welcome zero in is very part of that will become simply you got off seven and so that modelers or are will be equal to real party square which is zero and the mens rea party square there are three You're out of seven its whole square under roots so simply it will be cube root of seven. Now to get argument this is somewhere here that is only misery. Access angle theater will be bye bye to so argument of that will be bye bye to place to occupy where K belongs to the interior. Okay not principal argument. Principal argument makes the argument which should belong to the interval minus pi to pi minus pi is excluded and pies included. Okay so argument that will be. Uh huh When we plug in K equal to zero then only it will become by by two and by by two is the only principle argument because private belongs to the interval my inspire to buy. Okay no the polar form is our sister to Art is cube root of seven says bye bye to seize means called cedar placentas and theater. So these all are the answers. Okay these are the answers. Thank you


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