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

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Sum

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.

Concept: Cube Root of Unity
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Chapter 3: Complex Numbers - EXERCISE 3.3 [Page 42]

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