If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω 2 ) 100 + (1 - ω + ω 2 ) 100 equal to?

UPSC NDA II 2024 Mathematics Paper

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If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω²)¹⁰⁰ + (1 - ω + ω²)¹⁰⁰ equal to?

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