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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

∴ ω^{3} = 1 and 1 + ω + ω^{2} = 0

Also, 1 + ω^{2} = - ω, 1 + ω = - ω^{2} and ω + ω^{2} = – 1

`omega + 1/omega = (omega^2 + 1)/omega = (-omega)/omega` = – 1.

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