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Math Help - Complex Series

  1. #1
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    Complex Series

    Hi and thank you for providing such a opportunity.

    Question :



    I know this question makes the use of e^j0 = cos0 + jsin0 (0= theater) but I cant quite undrestand how.


    Last edited by Persia; April 10th 2007 at 02:34 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Persia View Post
    Hi and thank you for providing such a opportunity.

    Question :



    I know this question makes the use of e^j0 = cos0 + jsin0 (0= theater) but I cant quite undrestand how.

    sum(n=1..infty) 1/z^n = 1/(z-1) for |z|>1.

    Put z=3exp(i theta), then we have:

    sum(n=1..infty) (1/3^n) exp(-i theta) = 1/[3 exp(i theta)-1]

    Now take real parts so:

    Re sum(n=1..infty) (1/3^n) exp(-i n theta) = Re 1/[3 exp(i theta)-1]

    or:

    sum(n=1..infty) (1/3^n) cos(n theta) = Re 1/[3 exp(i theta)-1]

    So now just find the real part of the Right Hand Side to complete the
    problem.

    RonL
    Last edited by CaptainBlack; April 10th 2007 at 08:43 AM.
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    Thank you
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