Complex numbers

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If Z=x+2iy, then find Re(z*) Where z=x+iy is the formula and x=Re(z) and y=IM(z)
Re= real , IM=imag.
* is the conjugate

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\(z^*\) is obtained by reflecting the complex number over real axis it is called the conjugate of \(z\)
when you reflect something over real axis, notice that the real component is not changed
Here is how it says to do it: Re(z*) =Re(x-2iy) =x. Can you help me understand it that way?
just enter the part that is not attached to \(i\)
I thought the same thing until part B that wants Re(z^2). I know the right answer for it but cant get it.
z = x+2iy z^2 = (x+2iy)^2 = ?
But I thought it only wanted the real part. If you square all of it for this one, why did you only worry about the x in the other and not the imaginary 2iy in the other one?
because they are asking just the real part
Yea, so why is it not z^2, so z=x, so z^2 = x^2?
z is not x z is x+2iy
So what does the Re they specifify there mean?
to find the real part of z^2, first you need to find z^2
Ohh. Ohh. Ohh.
So can you let me work through it real quick?
sure
So I need (x+2iy)^2 first, which gives x^2+4iy-4y? is that right?
(x+2iy)^2 = x^2 + 4iy - 4y^2
How is the last part that?
I thought 2iy*2iy was 4i^2*y^2 Or -4y^3 Oh I understand.
(2iy)^2 = 4i^2y^2 = -4y^2
Oh so x^2-4y^2 is all the non imaginary stuff.
\(z = x+i2y\) \(z^2 = (x+2iy)^2 = \color{red}{x^2-4y^2} + i\color{purple}{4y}\)
yes x^2-4y^2 is the real part
THANK YOU x1,000,000,000
np:)
Wait, why does the book sayx^2+4ixy-4y^2? Where did the x in the 4ixy come from? @ganeshie8
right, \(z = x+i2y\) \(z^2 = (x+2iy)^2 = \color{red}{x^2-4y^2} + i\color{purple}{4xy}\)
we're just using the identity \[\large (\heartsuit + \spadesuit)^2~~ =~~ \heartsuit^2 + 2\heartsuit\spadesuit + \spadesuit^2 \]
|dw:1440213734204:dw| Sorry I'm so slow
|dw:1440213819660:dw|
yeppers. You came through again.
np

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