In my calculation, there exist some expressions like $-i e^{\frac{i k}{2}} \sqrt{-e^{-i k}}$, which are not simplified to be $1$, and makes further calculations rather complicated.
I tried to simplify the expression:
Simplify[-I Exp[(I k)/2] Sqrt[-Exp[-I k]]]
(* I E^((3 I k)/2) (-E^(-I k))^(3/2) *)
But these expressions are made lengthier using Mathematica. I find Mathematica does compute the square root of negative number:
Simplify[Sqrt[-1]]
(* I *)
But Mathematica doesn't combine them in the easiest way.
How is it possible to use Mathematica to simplify $-i e^{\frac{i k}{2}} \sqrt{-e^{-i k}}$ to $1$ in my calculation?