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Question: Answered & Verified by Expert
A value of $n$ such that $\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1$ is
MathematicsComplex NumberTS EAMCETTS EAMCET 2007
Options:
  • A $12$
  • B $3$
  • C $2$
  • D $1$
Solution:
1533 Upvotes Verified Answer
The correct answer is: $12$
Given,
$\begin{aligned} & \left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1 \\ & \left(\operatorname{cis} \frac{\pi}{6}\right)^n=1\end{aligned}$
$\therefore$ Only $n=12$ satisfies this equation.

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