Question

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

• A. $0,1$
• B. $1,1$
• C. $1,0$
• D. $-1,1$

Answer 1

The correct option is B $1,1$

Given $(1+\omega {)}^7=A+B\omega$

As we know that $1+\omega +{\omega }^2=0⟹1+\omega =-{\omega }^2$

So $(-{\omega }^2{)}^7=A+B\omega$

$⟹-{\omega }^{14}=A+B\omega$

$⟹-{\omega }^2=A+B\omega$

$⟹1+\omega =A+B\omega$

$⟹A=1,B=1$