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Complex number proof

  1. May 11, 2007 #1
    1. The problem statement, all variables and given/known data

    w=cos(theta) + isin(theta) where 0<theta<pi
    if the complex number w^2 + (5/w) -2 is purely imaginary, show that 2cos^2 x + 5 cos (theta) -3=0.
    Hence, find w.

    2. Relevant equations

    cos^2(theta) + sin^2 (theta) = 1

    3. The attempt at a solution

    im guessing to substitue w into the complex number.
  2. jcsd
  3. May 12, 2007 #2


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    Staff Emeritus
    Science Advisor

    Do you know that [itex]w^2= cos(2\theta)+ i sin(2\theta)[/itex] and that [itex]1/w= w^{-1}= cos(-\theta)+ i sin(-\theta)= cos(\theta)- i sin(\theta)[/itex]? Whoever assigned this problem certainly expects you to know that!
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