Question

If $|z+\overline{z}|+|z-\overline{z}|=2$, then z lies on.

• A. A straight line
• B. A square
• C. A circle
• D. Parabola

Answer 1

Answer: (A)

A straight line

Solution:- (A) A straight line

$|z+\overline{z}|+|z-\overline{z}|=2.....\left(1\right)$

Let $z=x+iy$

$\therefore \overline{z}=x-iy$

$|x+iy+x-iy|+|x+iy-x+iy|=2$

$\left|2x\right|+\left|2iy\right|=2$

$\sqrt{{\left(2x\right)}^2}+\sqrt{{\left(2y\right)}^2}=2$

$2x+2y=2$

Hence $z$ lies on the straight line.