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October 13th, 2017, 08:51 PM   #1
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Complex Numbers

Hello, I am kind of having trouble in how to express in terms of x and y . What are are steps and final solution.

I know that x = Re and y = Im but no idea how to do it.
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October 13th, 2017, 09:04 PM   #2
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Have you tried to find $\dfrac{z}{\bar{z}}$ ?
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October 13th, 2017, 09:07 PM   #3
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Have you tried to find $\dfrac{z}{\bar{z}}$ ?
Is $\dfrac{z}{\bar{z}}$ = x+iy/x-iy ? or am i wrong here ?
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October 13th, 2017, 09:11 PM   #4
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Yes.
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October 13th, 2017, 09:15 PM   #5
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I know what z and conguate of z equals to. But how do i get that in terms of x and y . Wont Re(z) = x and Re(conguate z) = x give me 1 just as for imaginary but -1. This would give me z = 1 - 1 = 0
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October 13th, 2017, 09:26 PM   #6
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Is the answer z = 1 + i2xy ?
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October 13th, 2017, 09:44 PM   #7
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Originally Posted by Robotboyx9 View Post
Hello, I am kind of having trouble in how to express in terms of x and y . What are are steps and final solution.

I know that x = Re and y = Im but no idea how to do it.
$z = x+i y$

$\begin{align*}

&Re \left( \dfrac{z}{\overline{z}}\right) = \\

&Re\left( \dfrac{x+i y}{x-i y}\right) = \\

&Re\left( \dfrac{(x+i y)^2}{x^2 + y^2}\right) = \\

&Re\left( \dfrac{x^2 - y^2 + 2 i x y }{x^2 + y^2}\right) = \\

&\dfrac{x^2 - y^2}{x^2 + y^2}

\end{align*}$

you should be able to easily do the other one using this as an example.
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