If α , β ∈ C are the distinct roots of the equation x 2 - x + 1 = 0 , then α 101 + β 107 is equal to

Step-by-step solution

x 2 - x + 1 = 0 Roots are - ω ,   - ω 2 . α 101 + β 107 = - ω 101 + - ω 2 107 = - ω 2 - ω   ∵ ω 3 = 1 = - ω 2 + ω = 1   ∵ 1 + ω + ω 2 = 0