I have tried to find out the branch cuts and branch points of the function $\sqrt(z^a +1)$, where $0<a<2$. The function can be written as $e^{\frac{1}{2}(\log(z^a+1))}$ and from here I have concluded following:
Branch points: $\{z: z^a+1=0\}$ and branch cuts: $\{z:\Re(z^a+1)\leq 0\}$.
Is my conclusion right? If so how to visualize the branch cuts explicitly? Otherwise how to find the branch points and cuts of the said function?
Thank you in advance.