A) \[\pi /5\]
B) \[2\pi /5\]
C) \[\pi /10\]
D) \[\pi /15\]
Correct Answer: C
Solution :
\[\sin \frac{\pi }{5}+i\,\left( 1-\cos \frac{\pi }{5} \right)\] \[=2\sin \frac{\pi }{10}\cos \frac{\pi }{10}+i2{{\sin }^{2}}\frac{\pi }{10}\] \[=2\sin \frac{\pi }{10}\left( \cos \frac{\pi }{10}+i\sin \,\frac{\pi }{10} \right)\] For amplitude, \[\tan \theta =\,\frac{\sin \frac{\pi }{10}}{\cos \frac{\pi }{10}}=\tan \frac{\pi }{10}\] Þ \[\theta =\frac{\pi }{10}\].
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