I don't know where to post this, so I'll put it here.

If $\displaystyle z=x+yi$ and $\displaystyle z^2=a+ib$ and a, b, x, and y are real, prove that

$\displaystyle 2x^2=\sqrt{a^2+b^2}+a$

How do i go about doing this? Other than that

$\displaystyle a=x^2-y^2$ and $\displaystyle b=2xy$

Thanks