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Nth roots of unity

  1. Sep 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that, if [tex]\omega[/tex] is an nth root of unity, then so are [tex]\overline{\omega}[/tex] and [tex]\omega^{r}[/tex] for every integer r.


    2. Relevant equations
    [tex]\omega[/tex]=r[tex]^{1/n}[/tex]e[tex]^{i((\theta+2\pi)/n)}[/tex]


    3. The attempt at a solution
    I got the first part and for [tex]\omega^{r}[/tex] I have it equals
    e[tex]^{i(r2\pi/n)}[/tex]
    but what more do I need to do/show to prove it's an nth root of unity?
     
  2. jcsd
  3. Sep 13, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    There's no need to use an explicit form for w. An nth root of unity satisfies w^n=1. Just use that. Take the conjugate and then raise both sides to the power r.
     
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