Q244 / 270 · NDA 2010 (Phase 2) · Mathematics

What is the value of $(-1+i \sqrt{3})^{48}$ ?

  • A
    1
  • B
    2
  • C
    $2^{24}$
  • Correct answer
    D
    $2^{48}$

Solution

$\begin{aligned} & \left\{2\left(-\frac{1}{2}+i \frac{\sqrt{3}}{2}\right\}^{48}\right. \\ & =2^{48}\left(\cos \frac{2 \pi}{3}+i \sin \frac{\pi}{3}\right)^{48} \\ & =2^{48}(\cos 32 \pi+i \sin 16 \pi) \\ & =2^{48}(1+0)=2^{48}\end{aligned}$

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

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