I have a question about the roots of complex numbers, ie., $\sqrt{z}$, $\sqrt[3]{z}$, etc. Obviously, these can be calculated using DeMoivre's Formula for complex exponentials, but is there any way to incorporate them as an analytic function, as has been done with $log(z)$ and $Log(z)$? I'm somewhat experienced in Complex Analysis (meaning I took a first course which went up to isolated singularities and the Residue Theorem) but I've never seen anything pertaining to this
Any ideas?