Question

If ω ( ≠ 1 ) is a cube root of unity an ( 1 + ω )^7 = A + Bω, then A and B are respectively the numbers 

Answer 1

for cube root of unity
1+ω=-ω²
therefore
(1+ω)^7=(-ω²)^7=-ω^14
as ω³=1
-ω^12(ω²)=-ω²=-(1+ω)=-ω-1
therefore A=-1,B=-1

Answer 2

the answerr is  a= 1 and b = -1.