Q. 26 D5.0( 3 Votes )

# State True of False for the following:The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).

True

Explanation:

Given |z – 1| = |z – i|

Putting z = x + iy,

|x – 1 + iy| = |x – i (1 – y) |

(x – 1)2 + y2 = x2 + (1 – y)2

x2 - 2x + 1 + y2 = x2 + 1 + y2 – 2y

-2x + 1 = 1 – 2y

-2x + 2y = 0

x – y = 0

Now, equation of a line through the points (1, 0) and (0, 1) is

x + y = 1

This line is perpendicular to the line x – y = 0.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Polar & Euler Form of Complex Numbers on Argand Plane32 mins
Interactive Quiz Time - Polar & Euler Form of complex number58 mins
Practice session | Argument of complex numbers61 mins
Modulus & Conjugate of Complex Number | Ready for a Quiz?48 mins
Questions on Modulus & Conjugate of Complex Number62 mins
Questions Based on Polar & Euler Form of Complex Number63 mins
Special Quiz on Argument of complex numbers56 mins
Polar & Euler Form of Complex Number on Argand Plane58 mins
Interactive Quiz on Quadratic Equations-0252 mins
Interactive Quiz on Quadratic Equations73 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses