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Question
If ω is a complex cube root of unity, find the value of `ω + 1/ω`
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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
`ω + 1/ω = (ω^2 + 1)/ω`
= `(-ω)/ω`
= – 1
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