if 1,w,w2 are cube roots of unity prove that (1-w+w2)5+(1+w-w2)5=32 - Maths - Complex Numbers and Quadratic Equations

Question

if 1,w,w2 are cube roots of unity prove that
(1-w+w2)5+(1+w-w​2)5=32

Xyz · Answer

This answer is very helpful
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5e215d5aa80d1%20jpeg">

if 1,w,w2 are cube roots of unity prove that (1-w+w2)5+(1+w-w​2)5=32