Question

If 1,omega,omega square are the cube roots of unity, then find the value of (1-omega +omega square)^5+(1+omega-omega square)^5​

Answer 1

Step-by-step explanation:

(1-w+w²)⁵+(1+w-w²)⁵

we know 1+w+w²=0===>1+w²=-w and 1+w=-w²

therefore (-w-w)⁵+(-w²-w²)⁵

(-2w)⁵+(-2w²)⁵

-32w⁵-32w¹⁰

-32w³.w²-32(w³)³.w

-32w²-32w (since w³=1)

-32(w²+w)

-32(-1) (1+w+w²=0===>w+w²=-1)

32