CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The locus of the complex number z satisfying |z−1|=|z−i| on the argand plane, is

A
a line passing through origin and (1,1)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
a circle of radius 1units
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a line passing through origin and (1,1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a circle of radius 12 units
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A a line passing through origin and (1,1)
|z1|=|zi|
z lies on perpendicular bisector of line segment joining the points A(1,0) and B(0,1)
Slope of AB is
mAB=0110=1
Slope of the perpendicular is
m=1
Midpoint of AB is
M=(12,12)

Therefore, the equation of the perpendicular bisector is
y12=1(x12)y=x

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometrical Representation of Algebra of Complex Numbers
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon