If 𝜔≠1 is a cube root of unit, and (1 + 𝜔)7 = A + B𝜔. Then (A, B) equals :

Engineering

Mathematics

Cube Roots of Unity

Question

If 𝜔≠1 is a cube root of unit, and (1 + 𝜔)⁷ = A + B𝜔. Then (A, B) equals :

(–1, 1)

(1, 1)

(0, 1)

(2, 0)

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(1 + 𝜔)⁷ = A + B𝜔

(–𝜔²)⁷ = A + B𝜔

– 𝜔¹⁴ = A + B𝜔

– 𝜔² = A + B𝜔

1 + 𝜔 = A + B𝜔

(A, B) = (1, 1)