If ω(≠1) is a cube root of unity, and (1+ω)⁷ = A + Bω. Then (A,B) equals: (0,1), (1,0), (-1,1), (1,1)

Let (1+ω)⁷ = A + Bω
As we know, 1 + ω + ω² = 0
∴ 1 + ω = -ω² , ω³ = 1
(-ω²)⁷ = A + Bω
-ω¹⁴ = A + Bω
(Since ω¹² = (ω³)⁴ = 1⁴ = 1)
-ω² = A + Bω
1 + ω = A + Bω (comparing)
∴ A = 1
B = 1