Question

State whether the following statement is true or false.

If $|z+\overline{z}|=|z-\overline{z}|$ then the locus of $z$ is pair of straight line.

• A. True
• B. False

Answer 1

The correct option is A True

Let$z=x+iy$

$|z+\overline{z}|=|z-\overline{z}|$

$⟹|2x|=|2y|$

$⟹|x|=|y|$

Therefore $x=y$ or $x=-y$ which is a pair of straight lines.