If $\omega(
eq 1)$ is a cube root of unity and $(1+\omega)^{7}=A+B \omega$ then $A$ and $B$ are res

Question

If $\omega(
eq 1)$ is a cube root of unity and $(1+\omega)^{7}=A+B \omega$ then $A$ and $B$ are respectively\

Professor PC Thomas Classes · Answer

(b) : $(1+\omega)^{7}=A+B \omega$\ $\Rightarrow \quad\left(-\omega^{2}ight)^{7}=A+B \omega\left(\because 1+\omega+\omega^{2}=0ight)$\ $\Rightarrow-\omega^{14}=A+B \omega \Rightarrow-\omega^{2}=A+B \omega$\ $\Rightarrow \quad 1+\omega=A+B \omega \Rightarrow A=1, B=1$.\