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