Simplify the following equation [Complex Numbers]

[jcurl]

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)

Homework Equations

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]

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?

 

[jcurl]

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?

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)

 

[Bacle]

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