If $\omega(
eq 1)$ is a cube root of unity, and $(1+\omega)^7=A+B \omega$. Then $(A, B)$ equals

Question

Aicharya · Accepted Answer

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

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