The points representing complex number $z$ for which $|z - 3| = |z - 5|$ lie on the locus given by

Question

Dr. Abubacker · Accepted Answer

(c)
Given, $|z - 3| = |z - 5|$
$\Rightarrow \ \ \ (z - 3)\left( \overline{z} - 3 \right) = (z - 5)(\overline{z} - 5)$
[on squaring both sides]
$\Rightarrow \ \ \ \ 2\overline{z} + 2z = 16\ \ \ \ \ \  \Rightarrow \ \ \ \ \ z + \overline{z} = 8$
$\Rightarrow \ \ \ 2x = 8\ \ \ \ \ \ \  \Rightarrow \ \ \ \ \ x = 4$
Hence, locus of $z$ is a straight line parallel to $y$-axis

Q. The points representing complex number $z$ for which $|z - 3| = |z - 5|$ lie on the locus given by

Explanation

Reviewed by Dr. Abubacker

Want more practice?