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Simplify the following equation [Complex Numbers]

  1. Oct 10, 2011 #1
    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:
    [itex] 1+cos(\theta)+cos(2\theta)+cos(3\theta)+....+cos(n\theta) [/itex]


    2. Relevant equations



    3. The attempt at a solution
    I have no idea where to start. My only guess would be to do this: [itex] \sum_{i=0}^n cos(n\theta) [/itex] but I feel like that's way to easy and not what he is asking for.
     
  2. jcsd
  3. Oct 10, 2011 #2

    Dick

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    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?
     
  4. Oct 10, 2011 #3
    That's what I was thinking, but I'm not sure how to only get the [itex] cos [/itex] value. Since [itex] e^{i\theta} = cos(\theta) + isin(\theta) [/itex]
     
  5. Oct 10, 2011 #4
    Hint: scroll up and read Dick's post carefully.
     
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