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Math Help - proof help

  1. #1
    ux0
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    proof help

    Let \zeta = e^{2\pi i/n}

    Prove that

    x^n-1=(x-1)(x-\zeta)(x-\zeta^2)...(x-\zeta^{n-1})


    And if n is odd, that


    x^n+1=(x+1)(x+\zeta)(x+\zeta^2)...(x+\zeta^{n-1})



    If i could get help on the first part i think i should be able to do the odd part.
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  2. #2
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    Quote Originally Posted by ux0 View Post
    Let \zeta = e^{2\pi i/n}

    Prove that

    x^n-1=(x-1)(x-\zeta)(x-\zeta^2)...(x-\zeta^{n-1})


    And if n is odd, that


    x^n+1=(x+1)(x+\zeta)(x+\zeta^2)...(x+\zeta^{n-1})



    If i could get help on the first part i think i should be able to do the odd part.

    For this you need to know, or hopefully to remember, how to find n-th roots of a complex number...it's a little long to explain it here.

    Tonio
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