Results 1 to 4 of 4

Math Help - roots of unity

  1. #1
    Junior Member
    Joined
    Aug 2008
    Posts
    27

    roots of unity

    The question asks, find the n solutions of z^n=1, which I got to be z=e^(2*i*k*Pi)/n, but where n is an odd positive integer. I now don't understand what the question is asking, is my answer wrong then? Any help would be much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2007
    Posts
    144
    Hi Happy Dancer,

    Your answer is correct: it doesn't matter whether n is odd or even the result still follows.

    You could say;

    The roots of z^n~=~1~ where n~=~2u+1 for some u~\in~\mathbb{Z} and u~\geq~1 are

    1,~w,~w^2,....,~w^{2u} where ~w~=~e^{\frac{2\pi i}{2u+1}}

    But that seems a tedious thing to do.
    Last edited by Sean12345; August 20th 2008 at 12:13 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2008
    Posts
    27
    Thanks, also whats the best way to prove that their sum is zero, is it just to state the formula for the geometric series?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Happy Dancer View Post
    Thanks, also whats the best way to prove that their sum is zero, is it just to state the formula for the geometric series?
    Read this: Root of unity - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Roots of unity
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: June 18th 2011, 01:51 PM
  2. nth roots of unity
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 1st 2010, 06:50 AM
  3. nth roots of unity
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 15th 2009, 12:09 AM
  4. nth roots of unity ???
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 7th 2009, 08:44 PM
  5. Roots of unity
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: December 30th 2008, 07:59 PM

Search Tags


/mathhelpforum @mathhelpforum