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

If z is a complex number that satisfies z2+z|z|+|z|2=0, then the locus of z is

A
a circle
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a straight line
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a pair of straight lines
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
an ellipse
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C a pair of straight lines
z2+z|z|+|z|2=0(z|z|)2+z|z|+1=0
Assuming z|z|=t
t2+t+1=0t=ω,ω2z|z|=ω,ω2z=ω|z| or z=ω2|z|x+iy=|z|(12±i32)x=|z|2, y=±3|z|2
Squaring both the sides,
4x2=x2+y2, 4y2=3(x2+y2)3x2y2=0

This represents a pair of straight lines.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon