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Question
If ω is a complex cube root of unity, then prove the following: (ω2 + ω - 1)3 = – 8
Solution
ω is a complex cube root of unity
∴ ω3 = 1 and 1 + ω + ω2 = 0
Also, 1 + ω2 = - ω, 1 + ω = - ω2
and ω + ω2 = – 1
L.H.S. = (ω2 + ω - 1)3
= (– 1 – 1)3
= (– 2)3
= – 8 = R.H.S.
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