Complex Numbers 5 Question 10
11. If $\omega(\neq 1)$ 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) $-1,1$
$(1995,2 M)$
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Answer:
Correct Answer: 11. (b)
Solution:
- $(1+\omega)^{7}=(1+\omega)(1+\omega)^{6}$
$$ \begin{aligned} & =(1+\omega)\left(-\omega^{2}\right)^{6}=1+\omega \\ & \Rightarrow \quad A+B \omega=1+\omega \\ & \Rightarrow \quad A=1, B=1 \end{aligned} $$
