(-3+i) ^ 53 where i ^ 2 =-1 is equal to [AMU 2000] - Vidyadip

MCQ

${{(-\sqrt{3}+i)}^{53}}$ where ${{i}^{2}}=-1$ is equal to [AMU 2000]

A
${{2}^{53}}(\sqrt{3}+2i)$
B
${{2}^{52}}(\sqrt{3}-i)$
✓
${{2}^{53}}\,\left( \frac{\sqrt{3}}{2}+\frac{1}{2}i \right)$
D
${{2}^{53}}(\sqrt{3}-i)$

✓

Answer

Correct option: C.

${{2}^{53}}\,\left( \frac{\sqrt{3}}{2}+\frac{1}{2}i \right)$

C

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