COMEDK · Maths · 3. Complex Number
Amplitude of the complex number \(i \sin \left(\frac{\pi}{19}\right)\) is
- A \(\frac{\pi}{19}\)
- B \(-\frac{\pi}{19}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{\pi}{2}-\frac{\pi}{19}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Let \(z=i \sin \frac{\pi}{19}\) or \(\quad z=0+i \sin \frac{\pi}{19}\) Let amplitude of \(z\) be \(\theta\), then \[ \sin \theta=\frac{\sin \frac{\pi}{19}}{\sqrt{0^{2}+\left(\sin \frac{\pi}{19}\right)^{2}}}\left[\because \sin \theta=\frac{b}{\sqrt{a^{2}+b^{2}}}\right] \] or…
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