Let $\sqrt.:= r^{1/2}[cos(\theta/2)+isin(\theta/2)], 0 \leq \theta < 2\pi$ define the the particular square root of a complex number.
For what values of z does the equation $\sqrt{z^2} = z$ hold?
I am really sorry, but this question has me stumped and I have no idea how to proceed, hence I couldn't show any working. If someone could please give me a hint.