Let $f(z) = (z^2-1)^\frac12$, and consider a branch $f_1(z)$: branch cut $[-1,1]$, with $f_2(z) = + ({x}^2-1)^\frac12$ for real $x > 1$. Find the limiting values of $f_2(z)$ above and below its branch cut and prove that $f_2(z)$ is odd.
- I was trying to assign angles in a continuous way as hinted but I don't know where to start. Can anyone give a hand? Any help is very appreciated!