Solving Complex Number Proof: w^2 + (5/w) - 2 = 0

[ahoy hoy]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

im guessing to substitue w into the complex number.

 

[HallsofIvy]

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