TS EAMCET · Maths · Complex Number
Let \(z=x+i y\) be a complex number, \(A=\{z /|z| \leq 2\} \text { and } B=\{z /(1-i) z+(1+i) \bar{z} \geq 4\}\) Then which one of the following options belongs to \(A \cap B\) ?
- A \(\sqrt{3}+\frac{1}{2} i\)
- B \(\frac{1}{2}+\frac{i}{2}\)
- C \(\sqrt{2}+\frac{i}{2}\)
- D \(2+2 i\)
Answer & Solution
Correct Answer
(A) \(\sqrt{3}+\frac{1}{2} i\)
Step-by-step Solution
Detailed explanation
We have, \(|z| \leq 2\) \(\begin{aligned} & \Rightarrow \quad(1-i)(x+i y)+(1+i)(x-i y) \geq 4 \\ & \Rightarrow \quad x+i y-i x+y+x-i y+i x+y \geq 4\end{aligned}\)…
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