Question

If $|z+\overline{z}|=|z-\overline{z}|$, then the locus of z is :

• A. A pair of straight lines
• B. A line
• C. A set of four straight line
• D. A circle

Answer 1

Answer: (A)

A pair of straight lines

$z=x+iy$

$\therefore |z+\overline{z}|=|x+iy+x-iy|=|2x|$

$\therefore |z-\overline{z}|=|(x+iy)-(x-iy)|=|2iy|$

$\therefore |z+\overline{z}|=|z-\overline{z}|\Rightarrow 2x=2iy$

$\therefore 2x-i2y=0$

$\therefore x=0;y=0\therefore pairofstraightlines$