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Question
If ω is a complex cube root of unity, find the value of (1 + ω2)3
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Solution
ω is the complex cube root of unity
∴ ω3 = 1 and 1 + ω + ω2 = 0
Also, 1 + ω2 = – ω, 1 + ω = – ω2 and ω + ω2 = – 1
(1 + ω2)3
= (– ω)3
= – ω3
= –1
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