Question

prove that (1-omega+omega^2)^7+(1+omega-omega^2)^7=128

Answer 1

Step-by-step explanation:

Given:

(1-w+w²)⁷+(1+w-w²)⁷=128

As we know that,

1+w+w²=0

And, w³=1

By applying these values in the equation,

→(-w-w)⁷+(-w²-w²)⁷

→(-2w)⁷+(-2w²)⁷

→-2⁷×w⁷+(-2⁷)×w¹⁴

→(-2⁷)w⁷(1+w²)

→(-128)w⁶.w(-w²)

→(-128)(-w³)

→128(w³)

→128(1)

→128

So, LHS=RHS

Hope it helps .....