If α, β ∈ C are the distinct roots of the equation x² - x + 1 = 0, then α¹⁰¹ + β¹⁰⁷ is equal to:<p></p>

Given equation: x² - x + 1 = 0
Solving it, we get
x = (1 ± i√3) / 2
Or, x = ω, ω²
α = -ω, β = -ω²
We know that, ω³ = 1, therefore
α¹⁰¹ + β¹⁰⁷ = (-ω)¹⁰¹ + (-ω²)¹⁰⁷ = (-ω)⁹⁹(-ω)² + (-ω²)¹⁰⁵(-ω²)² = -[ω² + ω] = -(sum of roots)
Hence, α¹⁰¹ + β¹⁰⁷ = 1

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Question:

If α, β ∈ C are the distinct roots of the equation x² - x + 1 = 0, then α¹⁰¹ + β¹⁰⁷ is equal to:

Solution: