Solving roots of complex number Given $z= \dfrac{i-1}{2}$. Evaluate $z^{1/2}$ and show the roots.
I got $z^{1/2}=\dfrac{1}{2^{1/4}}\left(\cos\dfrac{3\pi}{8} + i\sin\dfrac{3\pi}{8}\right)$
First of all is my $z^{1/2}$ correct? And secondly how to show the roots??
I would be glad and appreciated if someone could help me out.

Partly correct; what you have found is the principle value. A complete answer should be: $$z^{1/2}=\left(\frac{1}{\sqrt{2}}e^{i\frac{3\pi}{4}+2n\pi}\right)^{1/2}=\frac{1}{2^{1/4}}e^{i\frac{3\pi}{8}+n\pi}=\frac{1}{2^{1/4}}\left(\cos\left(\frac{3\pi}{8}+n\pi\right)+i\sin\left(\frac{3\pi}{8}+n\pi\right)\right)=\pm\frac{1}{2^{1/4}}\left(\cos\frac{3\pi}{8}+i\sin\frac{3\pi}{8}\right)$$
