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in Complex Numbers by (32.0k points)
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If ω is the complex cube root of unity, find the value of ω + 1/ω

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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

\(\omega+\frac1{\omega}=\frac{\omega^2+1}{\omega}=\frac{-\omega}{\omega}\) = -1

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