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A value of $n$ such that $\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1$ is
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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.
$\begin{aligned} & \left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1 \\ & \left(\operatorname{cis} \frac{\pi}{6}\right)^n=1\end{aligned}$
$\therefore$ Only $n=12$ satisfies this equation.
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