A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{6}\]
C) \[{{e}^{\pi /6}}\]
D) \[{{e}^{\pi /3}}\]
E) \[\frac{\pi }{3}\]
Correct Answer: E
Solution :
Given, \[z=\sqrt{3}+i,\] \[\arg ({{z}^{2}}{{e}^{z-i}})=\arg [(3-1+2\sqrt{3}i){{e}^{\sqrt{3}}}]\] \[=\arg [(2+2\sqrt{3}i){{e}^{\sqrt{3}}}]\] \[={{\tan }^{-1}}\left[ \frac{2\sqrt{3}}{2} \right]\] \[=\frac{\pi }{3}\]
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