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Complex Variables

  1. Dec 3, 2009 #1
    1. The problem statement, all variables and given/known data
    I'd like some help with 2 problems:

    Show by using Demoivre's theorem and the geometric series formula that the sum of all n values of z^(1/n) is zero when n >=2.
    Z is a complex number.

    Use the geometric series formula and Demoivre's theorem to show that:

    eq3.png


    2. Relevant equations

    the geometric series formula:
    eq1.png

    Demoivre's theorem

    eq2.png






    3. The attempt at a solution

    For the first part,I've tried to make z^(1/n) = p so that p^n = z ,but I had no success showing that the sum equals zero...
    For the second part I've made z= cos(theta) + i sin(theta) and I've obtained the left part of the formula,but I can't get the right part...

    I'd appreciate any help,because I don't seem to be going anywhere.
    Thank you in advance!
     
    Last edited: Dec 3, 2009
  2. jcsd
  3. Dec 3, 2009 #2

    Mark44

    Staff: Mentor

    If [itex]z = cos(\theta)[/itex], what is z2, z3, and so on?
     
  4. Dec 4, 2009 #3
    For the second question, a big hint is to equate equivalent terms.

    a + bi = c + di --> a = c, b = d

    Don't move things across the equals sign, but work on each side separately
     
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