Proof: Complex Number w^2+(5/w)-2=0 is Purely Imaginary

[ahoy hoy]

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

any input would be appreciated, thx.

 

[Office_Shredder]

I'm a bit confused... if w^2 + (5/w) -2 = 0 is purely imaginary... why do you need to say it's purely imaginary? Don't we already know it's zero? Or is w pure imaginary (in which case we just know cos(theta)=0)?

 

[ahoy hoy]

ahh good call. the complex number w^2 + (5/w) -2 is purely imaginary, doesn't necessarily equate to zero.