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If $\omega(\neq 1)$ is a cube root of unit, and $(1+\omega)^{7}=A+B \omega .$ Then $(A, B)$ equals :

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

Explanations

$(1+\omega)^{7}=\left(-\omega^{2}\right)^{7}=-\omega^{14}=-\omega^{2}$
$\quad=1+\omega=A+B \omega \Rightarrow A=1, B=1$

by Diamond (75,934 points)

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