Question

prove that:
1-ω+ω^2=1+ω-ω^2=4

Answer 1

1 - ω + ω² = -2ω,    as  1+ω²+ω = 0,  1+ω² = -ω
1 + ω - ω² = -2ω²    as 1 + ω = -ω²

So (1 - ω + ω²) (1 + ω - ω²) = -2ω * -2ω² = 4 ω³ = 4