Complex Numbers: Cube roots of unity application MCQ

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Cube roots of unity applicationMediumQuestion 230017

Question

If ω is a primitive cube root of unity, then (1 + ω − ω²)³ is:

−8

Since 1 + ω + ω² = 0, we have 1 + ω = −ω². So 1 + ω − ω² = −ω² − ω² = −2ω². Then (−2ω²)³ = −8ω⁶ = −8(ω³)² = −8(1)² = −8.