AP EAMCET · Maths · Complex Number
Let \(z\) and \(w\) be two complex numbers such that \(\bar{z}+i \bar{w}=0\) and \(\operatorname{Arg}(z w)=\pi\). Then, \(\operatorname{Arg} z=\)
- A \(\frac{3 \pi}{4}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{5 \pi}{4}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{3 \pi}{4}\)
Step-by-step Solution
Detailed explanation
Given, \(\bar{z}+i \bar{w}=0\) \(\Rightarrow \quad \bar{z}-i \bar{w}=0 \quad[\because \bar{i}=-i]\) \(\Rightarrow \quad \bar{z}-\overline{i w}=0 \quad\left[\because \overline{z_1 \cdot z_2}=\bar{z}_1 \cdot \bar{z}_2\right]\)…
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