AP EAMCET · Maths · Complex Number
If \(z_1=-\sqrt{3}+i\) and \(z_2=-\sqrt{3}-i\) then the principal amplitude of the complex number \(\frac{z_1}{z_2}\) is
- A \(\frac{\pi}{3}\)
- B \(\frac{5 \pi}{6}\)
- C \(\frac{-\pi}{3}\)
- D \(\frac{5 \pi}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{-\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(\frac{z_1}{z_2} = \frac{-\sqrt{3}+i}{-\sqrt{3}-i}\) \(= \frac{(-\sqrt{3}+i)^2}{(-\sqrt{3}-i)(-\sqrt{3}+i)} = \frac{3 - 2\sqrt{3}i + i^2}{(-\sqrt{3})^2 - i^2} = \frac{3 - 2\sqrt{3}i - 1}{3 - (-1)} = \frac{2 - 2\sqrt{3}i}{4} = \frac{1}{2} - \frac{\sqrt{3}}{2}i\)…
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