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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

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

4 views Answered 2023-02-05 15:29

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