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Demoivre's Theorem: Am I doing it right?

  1. Mar 3, 2007 #1
    1. The problem statement, all variables and given/known data
    Use Demoivre's Theorem to evaluate w^2, if w=3(cos30degs+ising30degs)
    PS, it's really pi/6, but I converted it to 30 degrees since I can't write on the screen..

    2. Relevant equations
    z^n=r^n(cos n*theta + i sin n*theta)

    3. The attempt at a solution

    w^2=3^2 (cos 2*30degs + i sin 2*30degs_
    w^2=9(0.5+i [square root of 3]/2)
    w^2=(9/2)+9i[square root of 3]/2

    I copied the test review answer key.. but I'm not sure if I copied it down right..
    The answer that I copied down was
    9[square root of 3]/2 + i9[square root of 3]/2..

    That answer would like like it would come from a 45deg thing.. but sinn and cosn are 60degs..

    Just making sure.. So has anyone seen where I went wrong?
    Last edited: Mar 3, 2007
  2. jcsd
  3. Mar 3, 2007 #2
    looks to be copied down wrong.
    Just don't use decimals, write 9/2, not 4.5
  4. Mar 3, 2007 #3
    I edited my initial post since I forgot the imaginary "i" part. And yes, I realize that 9/2 is 4.5. Anyone else NOT get 4.5[square root of 3] as opposed to just plain old 4.5 (9/2) for the "real" part?
  5. Mar 4, 2007 #4


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    You copied the answers down incorrectly. The correct answer is [tex]w^2=\frac{9}{2}+i\frac{9\sqrt{3}}{2}[/tex].
  6. Mar 4, 2007 #5
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