Complex Numbers: Roots of unity MCQ

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Roots of unityMediumQuestion 230010

Question

The cube roots of unity are 1, ω, ω². Then ω² + ω + 1 equals:

The three cube roots of unity satisfy x³ = 1, i.e., x³ − 1 = 0, i.e., (x−1)(x²+x+1) = 0. So ω and ω² satisfy x²+x+1 = 0, meaning 1 + ω + ω² = 0.