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Homework Help: De Moivre's Theorem (-12-5i)^-3

  1. Jan 1, 2010 #1
    1. The problem statement, all variables and given/known data

    Using De Moivres Theorem, solve (-12-5i)^-3

    2. Relevant equations



    3. The attempt at a solution

    The solution i get for this problem is different from the one given in the exercise text. This is 1/2197cis(8.241)

    Note: cis is equivalent to cos([tex]\Theta[/tex])+isin([tex]\Theta[/tex])
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 1, 2010 #2
    well you haven't actually written an equation down so there's nothing to solve.
    i'm assuming you meant to rewrite it in polar form and then use de moivre

    write -12-5i in polar form, that is z=r cis(theta)
    where r will be 13 if my mental pythagoras is correct and theta is arctan(y/x)

    then use de moivre (-12-5i)^(-3)=z^(-3)=r^(-3) cis(-3 theta)
     
  4. Jan 1, 2010 #3
    Remember that in the Argand diagram,-12-5i lies in the 3rd quadrant. Thus

    [tex]\theta = tan^{-1}(y/x) - \pi[/tex]
     
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