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

If z+8+z-8=16, where z is a complex number, then the point z will lie on


A

a circle

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

an ellipse

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

a straight line

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

None of the above

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

a straight line


Explanation for the correct option.

Find the locus of point z.

Let z=x+iy, then the equation z+8+z-8=16 can be written as:

z+8+z-8=16x+iy+8=16-x+iy-8x+82+iy=16-x-8+iyx+82+y2=16-x-82+y2

Now, square both sides.

x+82+y22=16-x-82+y22x2+16x+64+y2=256+x2-16x+64+y2-32x-82+y2-256+32x=-32x-82+y28-x=x-82+y2

Now again square both sides.

8-x2=x-82+y22x-82=x-82+y20=y20=y

So the complex number z lies on the equation y=0 which is an equation of straight line and represents the real axis in the complex plane.

So the point z will lie on a straight line.

Hence, the correct option is C.


flag
Suggest Corrections
thumbs-up
4
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Nature of Roots
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon