Q47 / 160 · AP EAMCET 2018 (22 Apr Shift 2) · Mathematics
The amplitude of $\sin \frac{\pi}{5}+i\left(1-\cos \frac{\pi}{5}\right)$ is
- A$\frac{\pi}{15}$
- Correct answerB$\frac{\pi}{10}$
- C$\frac{\pi}{5}$
- D$\frac{2 \pi}{5}$
Solution
Given complex number is,
$$
\begin{aligned}
& =\sin \frac{\pi}{5}+i\left(1-\cos \frac{\pi}{5}\right)=2 \sin \frac{\pi}{10} \cos \frac{\pi}{10}+i\left(2 \sin ^2 \frac{\pi}{10}\right) \\
& =2 \sin \frac{\pi}{10}\left[\cos \frac{\pi}{10}+i \sin \frac{\pi}{10}\right]
\end{aligned}
$$
So, amplitude of given complex number is $\frac{\pi}{10}$.
Hence, the correct answer is option: 'B'.