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JEE Advanced 2008Paper 1
Exam
JEE Advanced
Year
2008
Paper
Paper 1
Subject
Mathematics
Chapter
Complex Number

JEE Advanced 2008 · Paper 1 · Mathematics · Complex Number

Paragraph: Let A, B, C be three sets of complex numbers as defined...

Paragraph: Let A,B,CA, B, C be three sets of complex numbers as defined below. A={z;lm⁡z≥1};B={z:∣z−2−i∣=3};C={z:Re⁡((1−i)z)=2}A=\{z ; \operatorname{lm} z \geq 1\} ; B=\{z:|z-2-i|=3\} ; C=\{z: \operatorname{Re}((1-i) z)=\sqrt{2}\}.Question: Let zz be any point in A∩B∩CA \cap B \cap C. The ∣z+1−i∣2+∣z−5−i∣2|z+1-i|^2+|z-5-i|^2 lies between

Options

  1. A25 and 29
  2. B30 and 34
  3. C35 and 39
  4. D40 and 44

Correct answer

C. 35 and 39

Step-by-step solution

|z+1-i|^2+|z-5-i|^2=(x+1)^2+(y-1)^2+(x-5)^2+(y-1)^2 =2(x2+y2−4x−2y)+28=2(4)+28[\becausex2+y2−4x−2y=4]=36\begin{aligned}& =2\left(x^2+y²-4 x-2 y\right)+28 \\ & =2(4)+28 \\ & {\left[\becausex^2+y²-4 x-2 y=4\right]} \\ & =36 \\ & \end{aligned}
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