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

If zz1zz2=3, where z1 and z2 are fixed complex numbers and z is a variable complex number, then 'z' lies on a

A
Circle with centre as 9z1z28
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Circle with z2 as its interior point
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Circle with centre as 9z2z18
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Circle with z2 as its exterior point
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C Circle with centre as 9z2z18
Let P1,P2 be two points on the line joining the points A(α),B(β) which divides A and B in the ration 3:1 internally and externally



Now internal and external bisectors of APB will meet the line joining points A and B at P1 and P2, respectively.
Since,
AP1:P1BPA:PB3:1 (internal division)
and
AP2:P2BPA:PB3:1 (external division)
P1PP2=π2
Thus locus of 'P' is a circle having P1P2 as its diameter.
Now P1=z1+3z24,P2=3z2z12
Hence centre of circle will be =P1+P22
=9z2z18

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
This Is an Interesting Sum Part 1
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon