I'm having doubts about how to approach this problem.
I have a function $f(z)= \sqrt{z^2-1}$, where the argument of the complex inside the square root it's $\arg{(z^2-1)}=\arg{(z-1)}+\arg{(z+1)}$ and will be multivaluated according to the choice of each argument for $z-1$ and $z+1$.
How can I demonstrate that $z=\pm 1$ are branch points to $f(z)$?
All the examples in books I've found already assume $z=1$ or $z=-1$ are branch points.
Any advice will be helpful.