Question

The amplitude of $\sin \frac{\pi }{5}+i\left(1-\cos \frac{\pi }{5}\right)$ is

• A. $\pi /5$
• B. $2\pi /5$
• C. $\pi /10$
• D. $\pi /15$

Answer 1

Answer: (C)

$z=\sin \frac{\pi }{5}+i\left(1-\cos \frac{\pi }{5}\right)$
$=2\sin \frac{\pi }{10}\left(\cos \frac{\pi }{10}+i\sin \frac{\pi }{10}\right)$
$=2\sin \frac{\pi }{10}\cdot e^{i\frac{\pi }{10}}$
$\mathrm{Arg}(z)=\frac{\pi }{10}$