Results 1 to 2 of 2

Math Help - Roots of unit complex numbers

  1. #1
    Senior Member
    Joined
    Feb 2008
    Posts
    297

    Roots of unit complex numbers

    Show that if \omega is an nth root of unity ( \omega \neq 1 and n>1) then:

    \omega+\omega^2+...+\omega^n=0

    Would you do this (sum of G.P.)

    \omega\left(\dfrac{\omega^n -1}{\omega -1}\right)

    Since \omega^n=1 \Rightarrow \omega^n-1=0

    \Rightarrow \omega\left(\dfrac{\omega^n -1}{\omega -1}\right)=0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,564
    Thanks
    1425
    Looks good to me.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A is unitary iff the diagonals are complex unit numbers
    Posted in the Advanced Algebra Forum
    Replies: 13
    Last Post: November 5th 2011, 11:54 AM
  2. Complex Numbers & Unit Circle
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 9th 2011, 10:45 PM
  3. Complex Numbers, Unit Circle
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 27th 2010, 08:12 PM
  4. roots of complex numbers
    Posted in the Calculus Forum
    Replies: 8
    Last Post: November 9th 2008, 02:46 AM
  5. roots of complex numbers
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 13th 2008, 08:57 AM

Search Tags


/mathhelpforum @mathhelpforum