I have an expression of the form $(\frac{-1+e^{i\,N\,\phi}}{-1+e^{i \phi}})^n$.
I want to use mma to hopefully simplify it.
I have tried ComplexExpand[], PowerExpand[] with simplifying assumption in Refine[] that $N,\phi$ are real. But on using Simplify[] or FullSimplify[]. Either mma does nothing or gives a complicated answer.
a = PowerExpand[\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(N - 1\)]
\*SuperscriptBox[\(E\), \((I\ k\ \[Phi])\)]\)]
FullSimplify[ComplexExpand[a^n]]
Refine[FullSimplify[PowerExpand[a^n]],
Assumptions -> {N \[Element] Reals, \[Phi] \[Element] Reals}]
```