What is the magnitude of sum of complex exponentials?

Question

I know that $\ |Ae^{ix}|=A$

But I couldn't find a way to formulise the magnitude of sum of N exponentials that is:

$|\sum_{n=0}^{N} e^{inx}|=? \ $where $\ N \in \mathbb{Z^+}$

I will appreciate any help or hint.

Answer 1

The exponential may confuse you, but, if you let $e^{ix} = r$, then $\sum_{n=0}^{N} e^{inx} =\sum_{n=0}^{N} r^n$.

You should be able to sum this and then get its absolute value.