If w (≠1) is a cube root of unity and (1 + w)^7 = A + Bw

• Complex Numbers

If w (≠1) is a cube root of unity and (1 + w)⁷ = A + Bw. Then (A, B) equals to

1. (1, 1)
2. (1, 0)
3. (0, 1)
4. (-1, 1)

Solution

(1 + w)⁷ = A + Bw

(-w²)⁷ = A + Bw

-w¹⁴ = A + Bw

-w² = A + Bw

1 + w = A + Bw

The correct option is A.