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

Question

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

Dr. Abubacker · Accepted Answer

(b)
$(1 + \omega)^{7} = (1 + \omega)(1 + \omega)^{6}$
$= (1 + \omega)\left( - \omega^{2} \right)^{6} = (1 + \omega)$
$\Rightarrow \ A + B\omega = 1 + \omega$
$\Rightarrow \ A = 1,\ B = 1$

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

Explanation

Reviewed by Dr. Abubacker

Want more practice?