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Let S=S1 nn S2 nn S3, where s1={z in ...

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}`

A

0

B

1

C

2

D

`oo`

Text Solution

Verified by Experts

The correct Answer is:
B
Let z=x+iy
Set A corresponds to the region `y le 1`
Set B consists of points lying on the circle center at (2,1) and readius 3
i.e `x^2+y^2y-4`
Set C consistes of points lying on the `x+y=sqrt(2)`
Clearly there is only one point of the line `x+y=sqrt(2)` and circle` x^2+y^2-4x2y=4`
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