Results 1 to 3 of 3

Math Help - complex numbers involving demoivre

  1. #1
    Member
    Joined
    Dec 2008
    From
    Australia
    Posts
    161

    complex numbers involving demoivre

    show that:

     (1 + cos2\theta  + isin\theta )^n + (1+cos\theta  - isin\theta )^n = 2^{n+1}cos^n\frac{\theta }{2}cos\frac{n\theta }{2 }
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    for a complex number z = x+yi

    then z^n = r^ncis(n\theta) where

     r = \sqrt{x^2+y^2} and \tan(\theta) = \frac{y}{x}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by differentiate View Post
    show that:

     (1 + cos{\not2\theta}  + isin\theta )^n + (1+cos\theta  - isin\theta )^n = 2^{n+1}cos^n\frac{\theta }{2}cos\frac{n\theta }{2 } (The 2 on the left should not be there.)
    Use the identities 1+\cos\theta=2\cos^2\tfrac\theta2 and \sin\theta = 2\sin\tfrac\theta2\cos\tfrac\theta2.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Geometric Sum, involving complex numbers
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: June 4th 2011, 02:51 AM
  2. [SOLVED] A problem involving complex numbers in polar form
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 2nd 2010, 12:13 PM
  3. Simplifying an expression involving complex numbers.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 20th 2010, 04:31 AM
  4. Integration involving complex numbers
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 24th 2009, 09:24 PM
  5. equation involving complex numbers
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: March 29th 2009, 12:30 PM

Search Tags


/mathhelpforum @mathhelpforum