The roots of (2-2i) ^ 1/3 are - Vidyadip

MCQ

The roots of ${{(2-2i)}^{1/3}}$ are

✓
$\sqrt{2}\left( \cos \frac{\pi }{12}-i\sin \frac{\pi }{12} \right),\sqrt{2}\left( -\sin \frac{\pi }{12}+i\cos \frac{\pi }{12} \right),-1-i$
B
$\sqrt{2}\left( \cos \frac{\pi }{12}+i\sin \frac{\pi }{12} \right),\sqrt{2}\left( -\sin \frac{\pi }{12}-i\cos \frac{\pi }{12} \right)\,,\,1+i$
C
$1+\sqrt{2}i,-1-i,-2-2i$
D
None of the above

✓

Answer

Correct option: A.

$\sqrt{2}\left( \cos \frac{\pi }{12}-i\sin \frac{\pi }{12} \right),\sqrt{2}\left( -\sin \frac{\pi }{12}+i\cos \frac{\pi }{12} \right),-1-i$

A

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