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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 and let w be any point satisfying |w-2-i| < 3 . Then, |z|-|w|+3 lies between

Options

  1. A-6 and 3
  2. B-3 and 6
  3. C-6 and 6
  4. D-3 and 9

Correct answer

D. -3 and 9

Step-by-step solution

array ll & |w-(2+i)| < 3 & || w|-| 2+i|| < 3 & -3+ 5 < |w| < 3+ 5 & -3- 5 < -|w| < 3- 5 array Also, |z-(2+i)|=3 aligned -3+ 5 & |z| 3+ 5 -3 & < |z|-|w|+3 < 9 aligned

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