JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(A=\{z \in C:|z-2-i|=3\}\), \(B=\{z \in C: \operatorname{Re}(z-i z)=2\}\) and \(S=A \cap B\). Then \(\sum_{z \in S}|z|^2\) is equal to ________ .
- A 11
- B 33
- C 22
- D 55
Answer & Solution
Correct Answer
(C) 22
Step-by-step Solution
Detailed explanation
Let \(z=x+i y\) \(\begin{aligned} & A:|z-2-i|=3 \\ & |(x-2)+(y-1) i|=3 \\ & (x-2)^2+(y-1)^2=9 ....(1)\\ & B=\operatorname{Re}(z-i z)=2 \\ & \operatorname{Re}((x+y)+i(y-x))=2 \\ & x+y=2....(2) \end{aligned} .\) On solving (1) and (2) we get…
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