Results 1 to 4 of 4

Math Help - nth roots of unity

  1. #1
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301

    nth roots of unity

    We know the solutions of  z^{10} = 1 geometrically form a regular decagon. It it possible to generate the solutions of  z^{10} = 123 (for example) by applying some type of symmetric group action  G on the decagon?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Sampras View Post
    We know the solutions of  z^{10} = 1 geometrically form a regular decagon. It it possible to generate the solutions of  z^{10} = 123 (for example) by applying some type of symmetric group action  G on the decagon?
    ...why would we want to do something so complicated? Is there some other goal here?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301
    Quote Originally Posted by Jhevon View Post
    ...why would we want to do something so complicated? Is there some other goal here?

    No just wondering.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Sampras View Post
    No just wondering.
    Oh, well, I'd just interpret it as \left( \frac z{\sqrt[10]{123}}\right)^{10} = 1 and apply the first geometric interpretation, perhaps using a change of variable g = \frac z{\sqrt[10]{123}} to make it look like g^{10} = 1.

    Anyway, geometrically what would happen is that instead of your solutions lying on the circle of radius 1 in the complex plane, they will lie on the circle of radius \sqrt[10]{123}
    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, 12:51 PM
  2. nth roots of unity
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 1st 2010, 05:50 AM
  3. Roots of unity.
    Posted in the Algebra Forum
    Replies: 10
    Last Post: January 9th 2010, 06:05 PM
  4. nth roots of unity ???
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 7th 2009, 07:44 PM
  5. Roots of unity
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: December 30th 2008, 06:59 PM

Search Tags


/mathhelpforum @mathhelpforum