A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{\pi }{6}\]
Correct Answer: D
Solution :
Let \[z=\frac{1+i\sqrt{3}}{\sqrt{3}\,+i}\] \[=\frac{1+i\sqrt{3}}{(\sqrt{3}+i)}\times \frac{(\sqrt{3}-i)}{(\sqrt{3}-i)}\] \[=\frac{\sqrt{3}\,-i+3i+\sqrt{3}}{3+1}=\frac{\sqrt{3}+i}{2}\] amp \[(z)={{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\] \[=\frac{\pi }{6}\]You need to login to perform this action.
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