How can I simplify $|\sin(\sqrt{iz})/\sin(\sqrt{i\bar{z}})|$, where $z$ is a complex number?
What I did so far: let $\sqrt{iz}=u$, then $iz=u^2$, and $i\bar{z}=-\bar{u}^2$, so $\sqrt{i\bar{z}}=iu$ (I'm not sure about the last one!)
so: $\sin(\sqrt{iz})/\sin(\sqrt{i\bar{z}})=\sin(u)/\sin(iu)$
and now I can use the representation of $\sin(u)$ in terms of $e^{iu}$.
Anything wrong with the method above!
// I've been asked to simplify this expression, no mention for the branch!//
So, no help!