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If $ω (\neq 1)$ be a cube root of unity and $(1 + ω)^{7} = A + B ω$ , then A and B are respectively the numbers are

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0, 1

1, 1

1, 0

-1, 1

answer is B.

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Detailed Solution

Given

$\begin{aligned} (1 + ω)^{7} = A + B ω \\ \Rightarrow {(- ω^{2})}^{7} = A + B ω \\ \Rightarrow - ω^{4} = A + B ω \\ \Rightarrow - ω^{2} = A + B ω \\ \Rightarrow A + B ω + ω^{2} = 0 \\ \Rightarrow A = 1, B = 1 \end{aligned}$

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