Question

Amplitude of the complex number $i\, \sin \bigg( \frac{\pi}{19} \bigg)$ is

• A. $ \frac{\pi}{19}$
• B. $- \frac{\pi}{19}$
• C. $ \frac{\pi}{2}$
• D. $ \frac{\pi}{2} - \frac{\pi}{19}$

Answer 1

The Correct Option is C

Let $z = i \, \sin \frac{\pi}{19}$
or $z = 0 + i \, \sin \frac{\pi}{19}$
Let amplitude of $z$ be $\theta$ then
$\sin \theta =\frac{\sin \frac{\pi}{19}}{\sqrt{0^{2}+\left(\sin \frac{\pi }{19}\right)^{2}}} \left[\sin \theta =\frac{b}{\sqrt{a^{2}+b^{2}}}\right] $
or $\sin\theta =\frac{\sin \frac{\pi }{19}}{\sin \frac{\pi }{19}} =1 \Rightarrow \theta =\frac{\pi}{2}$