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