Simplify the following equation [Complex Numbers]

  • Thread starter jcurl
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  • #1
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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:
[itex] 1+cos(\theta)+cos(2\theta)+cos(3\theta)+....+cos(n\theta) [/itex]


Homework Equations





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.
 

Answers and Replies

  • #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?
 
  • #3
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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?

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]
 
  • #4
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Hint: scroll up and read Dick's post carefully.
 

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