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JEE Advanced2008MathematicsComplex NumberActual

Paragraph: Let A, 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 . Question: Let z be any point in A B C . The |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 aligned & =2 (x^2+y^2-4 x-2 y )+28 & =2(4)+28 & [ x^2+y^2-4 x-2 y=4 ] & =36 & aligned

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