# If ω is a complex cube root of unity, find the value of ω+1ω - Mathematics and Statistics

Sum

If ω is a complex cube root of unity, find the value of omega + 1/omega

#### 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.

Concept: Cube Root of Unity
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