October 13th, 2017, 08:51 PM  #1 
Newbie Joined: Sep 2017 From: Sydney Posts: 17 Thanks: 0  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. 
October 13th, 2017, 09:04 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,643 Thanks: 571 Math Focus: Yet to find out. 
Have you tried to find $\dfrac{z}{\bar{z}}$ ?

October 13th, 2017, 09:07 PM  #3 
Newbie Joined: Sep 2017 From: Sydney Posts: 17 Thanks: 0  
October 13th, 2017, 09:44 PM  #7  
Senior Member Joined: Sep 2015 From: USA Posts: 2,100 Thanks: 1093  Quote:
$\begin{align*} &Re \left( \dfrac{z}{\overline{z}}\right) = \\ &Re\left( \dfrac{x+i y}{xi y}\right) = \\ &Re\left( \dfrac{(x+i y)^2}{x^2 + y^2}\right) = \\ &Re\left( \dfrac{x^2  y^2 + 2 i x y }{x^2 + y^2}\right) = \\ &\dfrac{x^2  y^2}{x^2 + y^2} \end{align*}$ you should be able to easily do the other one using this as an example.  

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calc3, calculus3, complex, numbers 
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