A) \[\frac{2\pi }{5}\]
B) \[\frac{\pi }{5}\]
C) \[\frac{\pi }{15}\]
D) \[\frac{\pi }{10}\]
Correct Answer: D
Solution :
Let \[z=\sin \frac{\pi }{5}+i\left( 1-\cos \frac{\pi }{5} \right)\] Then, amp \[={{\tan }^{-1}}\left( \frac{1-\cos \frac{\pi }{5}}{\sin \frac{\pi }{5}} \right)\] \[={{\tan }^{-1}}\left( \frac{2{{\sin }^{2}}\pi /10}{2\sin \frac{\pi }{10}\cos \frac{\pi }{10}} \right)\] \[\left[ \begin{align} & 1-\cos 2\theta =2{{\sin }^{2}}\theta \\ & \sin 2\theta =2\sin \theta \cos \theta \\ \end{align} \right]\] \[={{\tan }^{-1}}\left( \tan \frac{\pi }{10} \right)\] \[=\frac{\pi }{10}\]
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