wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
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
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
20π3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
16π3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
32π3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
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

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Area under the Curve
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon