Question
Question: The complex numbers z=x+ iy which satisfy the equation \(\left| \frac{z - 5i}{z + 5i} \right| = 1\) ...
The complex numbers z=x+ iy which satisfy the equation z+5iz−5i=1 lie on
A
The x-axis
B
The straight line y = 5
C
A circle passing through the origin
D
None of these
Answer
The x-axis
Explanation
Solution
Sol. z+5iz−5i=1 ⇒ z would lie the right bisector of the line segment connecting the points 5i and –5i.
Thus z would lie on the x-axis