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

If the imaginary part of z−4z−2i is 0 , then the locus of z is

A
Ellipse
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Circle
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Straight line
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Parabola
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C Straight line
To find locus of z
If the imaginary part of z4z2i is 0
We have,
x+iy4x+iy2i
x4+iyx+i(y2)

=((x4)+iy)(x(y2)i)[x+i(y2)][xi(y2)]
=x2+y24x2y+i(2x+4y8)x2+(y2)2

=x2+y24x2yx2+(y2)2+i(2x+4y8)x2+(y2)2
If the imaginary part is 0, then we have
(2x+4y8)x2+(y2)2=0
2x+4y8=0
which represents equation of a straight line.
Hence , Option C

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