Question

To prove: (1+w-w^2)^6=64

Answer 1

1+ω+ω²=0

ω³=1

To prove: (1+ω-ω²)⁶=64

<> Replace 1+ω= -ω²

LHS= (-ω²-ω²)⁶=(-2ω²)⁶

=(-2)⁶(-ω)⁶

=2⁶(ω³)²=2⁶=64