A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{2}\]
C) \[0\]
D) \[\frac{\pi }{6}\]
Correct Answer: D
Solution :
\[\frac{1+\sqrt{3}i}{\sqrt{3}+i}\times \frac{\sqrt{3}-i}{\sqrt{3}-i}=\frac{\sqrt{3}-i+3i+\sqrt{3}}{3+1}\] \[=\frac{2\sqrt{3}}{4}+\frac{2i}{4}\] \[=\frac{\sqrt{3}}{2}+\frac{i}{2}\] \[\therefore \] \[\tan \theta =\frac{y}{x}=\frac{1/2}{\sqrt{3}/2}\] \[\Rightarrow \] \[\tan \theta =\frac{1}{\sqrt{3}}=\tan \frac{\pi }{6}\] \[\Rightarrow \] \[\theta =\frac{\pi }{6}\]
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