A) \[\sqrt{2}\left( \cos \frac{\pi }{12}-i\sin \frac{\pi }{12} \right),\sqrt{2}\left( -\sin \frac{\pi }{12}+i\cos \frac{\pi }{12} \right),-1-i\]
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
Correct Answer: A
Solution :
Using De Moivre's theorem \[{{(\cos \theta +i\sin \theta )}^{n}}=(\cos n\theta +i\sin n\theta )\] and putting \[n=0\], 1, 2 then we get required roots.
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