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Question

Let S=S1S2S3, where
S1={zC:|z|<4}, S2={zC:Im(z1+3i13i)>0} and S3={zC:Re z>0}

Area of S=

A
10π3
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B
20π3
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C
16π3
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D
32π3
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Solution

The correct option is B 20π3
Let z=x+iy
S1:x2+y2<16

S2:Im((x1)+i(y+3)1i3)>0
Im((x1)+i(y+3)1i3×1+i31+i3)>0
3(x1)+y+3>03x+y>0

S3:x>0
S=S1S2S3
Shaded area represents S.



Area of S
=12r2θ=12×42×5π6=20π3

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