COMEDK · Maths · 3. Complex Number
If \(z=\sqrt{3}+i\), then the argument of \(z^2 e^{z-i}\) is equal to
- A \(\dfrac{\pi}{6}\)
- B \(e^{\pi / 6}\)
- C \(e^{\pi / 3}\)
- D \(\dfrac{\pi}{3}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
Given \(z = \sqrt{3} + i\). Express \(z\) in polar form: \(z = r(\cos \theta + i \sin \theta)\), where \(r = |z| = \sqrt{(\sqrt{3})^2 + 1^2} = 2\) and \(\theta = \arg(z) = \tan^{-1}\left(\dfrac{1}{\sqrt{3}}\right) = \dfrac{\pi}{6}\). Thus, \(z = 2e^{i\pi/6}\). We need to find…
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