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Math Help - Complex Numbers Problem

  1. #1
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    Complex Numbers Problem

    I'm not sure what section to place this in.. but here it goes!

    How would I go about showing the following?:

    Show that if z is any nth root of unity other than unity itself, then
    1 + z + z^{2} + z^{3} + ... + z^{n - 1} = 0

    Thanks,

    James Elmore
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  2. #2
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    Quote Originally Posted by jameselmore91 View Post
    I'm not sure what section to place this in.. but here it goes!

    How would I go about showing the following?:

    Show that if z is any nth root of unity other than unity itself, then
    1 + z + z^{2} + z^{3} + ... + z^{n - 1} = 0

    Thanks,

    James Elmore
    Consider the solution to z^n - 1 = 0 by first factorising z^n - 1.
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