# Simplify the following equation [Complex Numbers]

## Homework Statement

I'm in differential equations right now and we are about to start Laplace Transforms. Our homework is over complex numbers:

Simplify the following equation:
$1+cos(\theta)+cos(2\theta)+cos(3\theta)+....+cos(n\theta)$

## The Attempt at a Solution

I have no idea where to start. My only guess would be to do this: $\sum_{i=0}^n cos(n\theta)$ but I feel like that's way to easy and not what he is asking for.

Dick
That's what I was thinking, but I'm not sure how to only get the $cos$ value. Since $e^{i\theta} = cos(\theta) + isin(\theta)$