TS EAMCET · Maths · Complex Number
The amplitude of the complex number \(\frac{(\sqrt{3}+i)(1-\sqrt{3} i)}{(-1+i)(-1-i)}\) is
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{3}\)
- C \(-\frac{5\pi}{12}\)
- D \(-\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(D) \(-\frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
\(Z = \frac{(\sqrt{3}+i)(1-\sqrt{3} i)}{(-1+i)(-1-i)}\) \(Z = \frac{(\sqrt{3} - 3i + i - \sqrt{3}i^2)}{1 - i^2}\) \(Z = \frac{(\sqrt{3} - 2i + \sqrt{3})}{1 - (-1)}\) \(Z = \frac{2\sqrt{3} - 2i}{2}\) \(Z = \sqrt{3} - i\) \(\text{Amplitude} = \text{arg}(\sqrt{3} - i)\)…
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