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4-1.Complex numbers
easy
$\sin \frac{\pi }{5} + i\,\left( {1 - \cos \frac{\pi }{5}} \right)$ का कोणांक होगा
A
$\pi /5$
B
$2\pi /5$
C
$\pi /10$
D
$\pi /15$
Solution
(c) $\sin \frac{\pi }{5} + i\,\left( {1 – \cos \frac{\pi }{5}} \right)$ $ = 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)$
कोणांक के लिए $\tan \theta = \,\frac{{\sin \frac{\pi }{{10}}}}{{\cos \frac{\pi }{{10}}}} = \tan \frac{\pi }{{10}}$
$⇒ \theta = \frac{\pi }{{10}}$.
Standard 11
Mathematics
