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Math Help - Complex Numbers Problem

  1. #1
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    Complex Numbers Problem

    Hey

    can some one tel me how do i go about solving this question

    Let m be a positive fixed interger and l be an integer that is not divisible by m

    prove

    1 + w^l + w^2l + .... + w^(m-1)l = 0

    all the w's have subscript "m".


    Thanks
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  2. #2
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    Quote Originally Posted by flaming View Post

    1 + w^l + w^2l + .... + w^(m-1)l = 0
    I assume that \omega = e^{2\pi i/m}

    Then, \omega^l = e^{2\pi il/m}\not = 1 since m\not | l.

    Now use geometric sum, \frac{1 - (\omega^l )^{m}}{1-\omega^l} = 0.
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