A) \[\cos \frac{\pi }{3}+i\,\sin \frac{\pi }{3}\]
B) \[\cos \frac{\pi }{2}+i\,\sin \frac{\pi }{2}\]
C) \[\sin \frac{\pi }{6}+i\,\cos \frac{\pi }{6}\]
D) \[\cos \frac{\pi }{6}+i\,\sin \frac{\pi }{6}\]
Correct Answer: D
Solution :
\[{{x}^{2}}-\sqrt{3}x+1=0\] Þ \[\,x=\frac{\sqrt{3}\pm \sqrt{3-4}}{2}\] Þ \[x=\frac{\sqrt{3}\pm i}{2}\]\[=\frac{\sqrt{3}}{2}\pm \frac{i}{2}\] Þ \[x=\cos \left( \frac{\pi }{6} \right)+i\sin \left( \frac{\pi }{6} \right)\] [Taking +ve sign]
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