Find all couple $(x,y)$ for satisfy $\frac{x+iy}{x-iy}=(x-iy)$ I have a problem to solve this exercise, I hope someone help me.
Find all couple $(x,y)$ for satisfy $\frac{x+iy}{x-iy}=(x-iy)$

$\frac{x+iy}{x-iy}=\frac{(x+iy)^2}{(x-iy)(x+iy)}=\frac{(x+iy)^2}{x^2+y^2}=\frac{x^2-y^2}{x^2+y^2}+i\frac{2xy}{x^2+y^2}$
Then you have to impose 
$x=\frac{x^2-y^2}{x^2+y^2}$  
$y=\frac{2xy}{x^2+y^2}$
and solve the system.
