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Homework Help: Complex numbers and induction

  1. Sep 20, 2008 #1
    1. The problem statement, all variables and given/known dataIf z is a non-real complex number such that z+1/z=2costheta, prove that z^n+1/z^n=2cosntheta for any posistive integer n



    2. Relevant equations
    I think the process of induction would work, but im not quite sure how to do that with all of the unknowns, would i just treat costheta as a constant number


    3. The attempt at a solution
     
  2. jcsd
  3. Sep 20, 2008 #2

    olgranpappy

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    Homework Helper

    Apparently
    [tex]
    z=e^{i\theta}
    [/tex]
    ...does that help?
     
  4. Sep 20, 2008 #3

    rock.freak667

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    Homework Helper

    If z=cosx+isinx, what is z^n?
     
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