wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Complex numbers which satisfy both the equations |z1i|=2 and |z+1+i|=2 is/are

A
(1+78)+i(178)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(1+74)+i(174)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(178)+i(1+78)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(174)+i(1+74)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D (174)+i(1+74)
The given equation represents circles
(x1)2+(y1)2=2
and (x+1)2+(y+1)2=4

C1(1,1),r1=2,C2(1,1),r2=2
C1C2=8=2.8,r1+r2=2+2=3.41
C1C2<r1+r2 and also C1C2>r2r1 and hence the two circles are intersecting at two points. The common two points will satisfy both.
Solving both equations,we get intersection points as (1+74)+i(174) and (174)+i(1+74)

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