Find the area of the region common to the sets S1={z∈C: |z|<4}, S2={z∈C:Im[(z-1+√3i)/(1-√3i)]>0} and S3={z∈C: Re z>0}.

Question

Find the area of the region common to the sets S1={z∈C: |z|<4}, S2={z∈C:Im[(z-1+√3i)/(1-√3i)]>0} and S3={z∈C: Re z>0}.

1 Answer

Sebastian · Answer 1 · 2022-01-12T01:19:57+0000

Correct option is (b) 20π/3

Easiest explanation: S1: |z|<4, z lies inside the circle of radius 4; S2: √3x+y>0, z lies above the line √3x+y=0; S3: Re(z)>0, z lies to the right of the imaginary circle. Therefore, required area=π×4^2/4+π×4^2/6=20π/3.

Find the area of the region common to the sets S1={z∈C: |z|<4}, S2={z∈C:Im[(z-1+√3i)/(1-√3i)]>0} and S3={z∈C: Re z>0}.

Please log in or register to add a comment.

Please log in or register to answer this question.

1 Answer

Please log in or register to add a comment.

Related questions

Most popular tags

Find the area of the region common to the sets S1={z∈C: &vert;z&vert;<4}, S2={z∈C:Im[(z-1+√3i)/(1-√3i)]>0} and S3={z∈C: Re z>0}.

Please log in or register to add a comment.

Please log in or register to answer this question.

1 Answer

Please log in or register to add a comment.

Related questions

Most popular tags

Find the area of the region common to the sets S1={z∈C: |z|<4}, S2={z∈C:Im[(z-1+√3i)/(1-√3i)]>0} and S3={z∈C: Re z>0}.