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Question
If ω is a complex cube root of unity, find the value of ω2 + ω3 + ω4.
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
ω2 + ω3 + ω4
= ω2 (1 + ω + ω2) = ω2(0) = 0
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