Complex Numbers 2 Question 21
22.
The complex numbers $z=x+i y$ which satisfy the equation $\frac{z-5 i}{z+5 i}=1$, lie on
(1981, 2M)
(a) the $X$-axis
(b) the straight line $y=5$
(c) a circle passing through the origin
(d) None of the above
Show Answer
Answer:
Correct Answer: 22. (a)
Solution:
- Given, $\left|\frac{z-5 i}{z+5 i}\right|=1 \Rightarrow|z-5 i|=|z+5 i|$
$\left[\because\right.$ if $\left|z-z _1\right|=\left|z-z _2\right|$, then it is a perpendicular bisector of $z_1$ and $z_2$]
$\therefore$ Perpendicular bisector of $(0,5)$ and $(0,-5)$ is $X$-axis.
