SOLUTION —
$\sin \frac{\pi}{5}+i\left(1-\cos \frac{\pi}{5}\right)$
$=2 \sin \frac{\pi}{10} \cos \frac{\pi}{10}+i 2 \sin ^2 \frac{\pi}{10}$
$=2 \sin \frac{\pi}{10}\left(\cos \frac{\pi}{10}+i \sin \frac{\pi}{10}\right)$
For amplitude :
$\begin{aligned} \tan \theta & =\frac{\sin \frac{\pi}{10}}{\cos \frac{\pi}{10}}=\tan \frac{\pi}{10} \\ \Rightarrow \quad \theta & =\frac{\pi}{10}\end{aligned}$
So, The correct option will be (C).