How to find branch point of z^(-1/2)

Question

I know branch points are the point where $z^{-1/2} =0$ or $z^{-1/2} =\infty$, so for this I think $z$ should be $\infty$ for $z^{-1/2}$ to go $\infty$?? However for $z^{-1/2}$ to be equal $0$, I couldn't find a point where $z^{-1/2}$ goes to zero because when I put $z=0$, $z^{-1/2}$ is undefined. What should I do in this case to find $z^{-1/2}=0$??

Answer 1

The branch point you've already found is the only branch point, as $z^\frac{-1}2=0$ has no solutions.