Results 1 to 2 of 2

Thread: Summation of complex numbers

  1. #1
    Senior Member I-Think's Avatar
    Apr 2009

    Summation of complex numbers

    Given that  w_n=3^{-n}cos2n\theta for n=1,2,3... use De Moivre's Theorem to show that


    I am really hopelessly lost on this question.
    Help is greatly appreciated.
    Thanks in advance.
    Last edited by I-Think; Nov 2nd 2009 at 03:03 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Jun 2007
    Medgidia, Romania
    Let S_1=1+\frac{1}{3}\cos 2\theta+\frac{1}{3^2}\cos 4\theta+\ldots+\frac{1}{3^n}\cos 2n\theta

    and S_2=\frac{1}{3}\sin 2\theta+\frac{1}{3^2}\sin 4\theta+\ldots+\frac{1}{3^n}\sin 2n\theta

    Then S_1+iS_2=1+\frac{1}{3}(\cos 2\theta+i\sin 2\theta)+\frac{1}{3^2}(\cos 4\theta+i\sin 4\theta)+\ldots+\frac{1}{3^n}(\cos 2n\theta+i\sin 2n\theta)

    Let z=\frac{1}{3}(\cos 2\theta+i\sin 2\theta)

    Then S_1+iS_2=1+z+z^2+\ldots+z^n

    Now use the sum of a geometric progression and put the right hand member in the form A+Bi. Then S_1=A, \ S_2=B
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. raising complex numbers to complex exponents?
    Posted in the Advanced Math Topics Forum
    Replies: 10
    Last Post: Mar 25th 2011, 11:02 PM
  2. Replies: 1
    Last Post: Sep 27th 2010, 04:14 PM
  3. Proving numbers in sequences and summation
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Nov 16th 2009, 04:13 PM
  4. Replies: 2
    Last Post: Feb 7th 2009, 07:12 PM
  5. Replies: 1
    Last Post: May 24th 2007, 04:49 AM

Search Tags

/mathhelpforum @mathhelpforum