If \(\omega^3 = 1\) and \(\omega \neq 1\), then compute \((1 - \omega + \omega^2)(1 + \omega - \omega^2)\).
+128474 Note that
w^3 = 1
w^3 - 1 = 0
(w - 1) (w^2 + w + 1) = 0
So either
w - 1 = 0 reject because w cannot = 1 or
w^2 + w + 1 = 0
So.....
( 1 - w + w^2) ( 1 + w - w^2) =
[ ( 1 + w + w^2) - 2w ] [ (1 + w + w^2) - 2w^2 ] =
[ ( 0) - 2w ] [ (0) - 2w^2 ] =
[ -2w ] [ -2w^2 ] =
4w^3 =
4(1) =
4
