MHT CET · Maths · Complex Number
If \(\omega\) is complex cube root of unity and \((1+\omega)^7=\mathrm{A}+\mathrm{B} \omega\), then values of A and B are, respectively.
- A 0,1
- B 1,0
- C 1,1
- D \(-1,1\)
Answer & Solution
Correct Answer
(C) 1,1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (1+\omega)^7=\mathrm{A}+\mathrm{B} \omega \\ & \therefore \mathrm{A}+\mathrm{B} \omega=\left(-\omega^2\right)^7 \quad \ldots\left(\because 1+\omega+\omega^2=0\right] \\ & =(-1) \omega^{14}=-\omega^{12} \omega^2=-\omega^2=(1+\omega) \\ & \therefore A=1, B=1\end{aligned}\)
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