Let `S=S_1 nn S_2 nn S_3`, where `s_1={z in C :|z|<4}, S_2={z in C :ln[(z-1+sqrt(3)i)/(1-sqrt(31))]>0} and `
`S_3={z in C : Re z > 0}` Area of S=

Options

A. 25 and 29
B. 30 and 34
C. 35 and 39
D. 40 and 44

Answer

C

Explanation

Clearly, P(z) is the only poin in `A frown B frown C` satisfying `|z-(2+i)|=3`. We observe that `z_(1)=-1+i` and `z_(2)=5+i` both lie on the circle `|z-(2+i)|=3`, and their mid-point is the center of the circle. So, `A(z_(1))`and `B(z_(2))` are the end-points of a diameter of the circle `|z-(2+i)|=3`
`|z+1-i|^(2)+|z-5-i|^(2)=QA^(2)+QB^(2)=AB^(2)=36`