Determine the domain-sets of $$ Log(e^z-e^{-z})$$
I only know that $e^z-e^{-z} > 0$ and so z must be positive. Also, $e^z = e^{x+iy} $
The solution is $\Bbb{C}$ \ { $k \pi i | k \in \Bbb{Z}$ }
I don't understand the steps that will lead to this. Is there some other theory that I should know? Any help is appreciated.