# Homework Help: Simplify the following equation [Complex Numbers]

1. Oct 10, 2011

### jcurl

1. The problem statement, all variables and given/known data
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:
$1+cos(\theta)+cos(2\theta)+cos(3\theta)+....+cos(n\theta)$

2. Relevant equations

3. 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.

2. Oct 10, 2011

### Dick

If you are going to start Laplace transforms, you likely know about complex numbers. cos(n*theta) is the real part of exp(i*n*theta), yes? Can you relate your question to a geometric series?

3. Oct 10, 2011

### jcurl

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

4. Oct 10, 2011

### Bacle

Hint: scroll up and read Dick's post carefully.