Q63 / 160 · AP EAMCET 2007 · Mathematics

A value of $n$ such that $\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1$ is

  • Correct answer
    A
    $12$
  • B
    $3$
  • C
    $2$
  • D
    $1$

Solution

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.

Hence, the correct answer is option: 'A'.

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