1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook