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Let S=S1 cap S2 cap S3 where S1={z i...

Let `S=S_1 cap S_2 cap S_3` where
`S_1={z in C:|z| lt 4"}",S_2={z in C: lm[(z-1+sqrt(3)i)/(1-sqrt(3)i)]gt0}` and `S_3:{z in : Re z lt 0 }`
Let z be any point in `A cap B cap C`
The `|z+1-i|^2+|z-5-i|^2` lies between

A

25 and 29

B

30 and 34

C

35 and 39

D

40 and 44

Text Solution

Verified by Experts

The correct Answer is:
C
`|z+1-i|^2+|z-5-i|^2`
= `(x+1)^2 +(y-1)^2+(x-5)^2+(y-1)^2`
`=2(x^2+y^2-4x-2y)+28`
`=2(4)+28=36 " "[ because x^2+y^2-4x-2y =4]`
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