wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
Question

Let z=x+iy be a complex number, where x and y are real numbers. Let A and B be the sets defined by A={z:|z|2} and B={z:(1i)z+(1+i)¯¯¯z41} . Find the area of region AB.

A
3π2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3π+2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
π+2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
π2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is C π2
z=x+iy
A={z:|z|2}
x2+y22
or x2+y24
z lies on or inside the circle x2+y2=4
B={z:(1i)z+(1+i)¯¯¯z4}
(1i)(x+iy)+(1+i)(xiy)4
x+iyix+y+xiy+ix+y4
x+y2
Area of region AB is the shaded region shown in Fig. 3.19
Area = π(2)2412×2×2=π2
Ans: D
247490_133434_ans.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Representation and Trigonometric Form
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon