Question

The argument of the complex number $\sin \frac{6\pi }{5}+i(1+\cos \frac{6\pi }{5})$ is

• A. $\frac{6\pi }{5}$
• B. $\frac{5\pi }{6}$
• C. $\frac{9\pi }{10}$
• D. $\frac{2\pi }{5}$

Answer 1

The correct option is C $\frac{9\pi }{10}$

$\sin \frac{6\pi }{5}+i(1+\cos \frac{6\pi }{5})$
$=2\sin \frac{3\pi }{5}\cos \frac{3\pi }{5}+2i{\cos }^2\frac{3\pi }{5}$
$=-2\cos \frac{3\pi }{5}(-\sin \frac{3\pi }{5}-i\cos \frac{3\pi }{5})$
$=-2\cos \frac{3\pi }{5}(\cos \frac{9\pi }{10}+i\sin \frac{9\pi }{10})$
So argument is $\frac{9\pi }{10}$