# Complex number proof

1. May 11, 2007

### ahoy hoy

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. May 12, 2007

### HallsofIvy

Staff Emeritus
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!