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Math Help - Roots of unity

  1. #1
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    Roots of unity

    Hello guys...we know that the roots of unity are for that example z^n=1 possible just for n = all positive numbers
    what would happen if n = 0 or any non positive number?


    thanks
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  2. #2
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    Re: Roots of unity

    Quote Originally Posted by domenfrandolic View Post
    Hello guys...we know that the roots of unity are for that example z^n=1 possible just for n = all positive numbers
    what would happen if n = 0 or any non positive number?


    thanks

    z^{-n}=\frac{1}{z^n}
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    Re: Roots of unity

    Quote Originally Posted by domenfrandolic View Post
    Hello guys...we know that the roots of unity are for that example z^n=1 possible just for n = all positive numbers
    what would happen if n = 0 or any non positive number?
    First, realize that n is an integer.

    Second, if n=0 then \frac{1}{n} is not defined. So that is take n care of.

    Third, if n\in\mathbb{Z}^- we deal the nth root of the multiplicative inverse.
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    Re: Roots of unity

    hm...ok that makes sense that it comes to be 1/z^n=1...but like what happens then?how do i find solutions?are the same rools of the roots of unity applied?will we have for z^n=1 where n=-3 as an example three answers in a unit circle?
    thanks
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    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Roots of unity

    Quote Originally Posted by domenfrandolic View Post
    hm...ok that makes sense that it comes to be 1/z^n=1...but like what happens then?how do i find solutions?are the same rools of the roots of unity applied?will we have for z^n=1 where n=-3 as an example three answers in a unit circle?
    thanks
    1/z^n=1 <==> z^n=1
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