Complex Numbers And Quadratic Equations question 117
Question: The amplitude of $ \sin \frac{\pi }{5}+i( 1-\cos \frac{\pi }{5} ) $ [Karnataka CET 2003]
Options:
A) $ \pi /5 $
B) $ 2\pi /5 $
C) $ \pi /10 $
D) $ \pi /15 $
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Answer:
Correct Answer: C
Solution:
$ \sin \frac{\pi }{5}+i( 1-\cos \frac{\pi }{5} ) $ $ =2\sin \frac{\pi }{10}\cos \frac{\pi }{10}+i2{{\sin }^{2}}\frac{\pi }{10} $ $ =2\sin \frac{\pi }{10}( \cos \frac{\pi }{10}+i\sin \frac{\pi }{10} ) $ For amplitude, $ \tan \theta =\frac{\sin \frac{\pi }{10}}{\cos \frac{\pi }{10}}=\tan \frac{\pi }{10} $
Þ $ \theta =\frac{\pi }{10} $ .
BETA
