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
- A25 and 29
- B30 and 34
- C35 and 39
- 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