I am trying to plot certain holomorphic functions that contain square and higher roots. In the complex analysis sense, the function $f:z\mapsto z^\alpha$ for some $\alpha\in\mathbb C$ has a phase factor $e^{2\pi i\alpha}$ at $z=0$, which means that on a small circular path around $0$ the function $f$ picks up this factor. Is there a way to implement this in Mathematica?

For instance, 

 g[z_] = z^4;
 Sqrt[g[Exp[Pi I/2]]]
gives 1 as a result, where I would like Mathematica to keep the phase $g(e^{\pi i/2})=e^{2\pi i}$ and then compute 
$$\sqrt{g(e^{\pi i/2})}=e^{\pi i}=-1.$$
With Sqrt or $(\cdot)^{1/2}$ this does not seem possible, as they pick the principal square roots.
Many thanks for your help!