AP EAMCET · Maths · Complex Number
Let \(z_1, z_2\) be two complex numbers such that \(\bar{z}_1-i \bar{z}_2=0\) and \(\arg \left(z_1 z_2\right)=\frac{3 \pi}{4}\), then \(\arg \left(z_1\right)=\)
- A \(\frac{\pi}{4}\)
- B \(\frac{-\pi}{8}\)
- C \(\frac{\pi}{8}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{8}\)
Step-by-step Solution
Detailed explanation
Given \(\bar{z}_1-i \bar{z}_2=0\) \(\begin{array}{ll} \Rightarrow & \bar{z}_1=i \bar{z}_2 \\ \Rightarrow & \bar{z}_1=\overline{i z_2} \\ \Rightarrow & z_1=-i z_2 \end{array}\) Clearly argument of \(z_1=\) argument of \(z_2-\frac{\pi}{2}\) or argument \(z_1=\) argument…
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