Question

The closest distance of the origin from a curve given as $a\overline{z}+\overline{a}z+a\overline{a}=0$ (a is a complex number) is

• A. 1
• B.
• C.
• D.

Answer 1

The correct option is B

The closest distance = length of the perpendicular from the origin on the line $a\overline{z}+\overline{z}+a\overline{a}=0$
=$\frac{a\left(0\right)+\overline{a}|0|+a\overline{a}}{2|a|}=\frac{|a{|}^2}{2|a|}=\frac{|a|}{2}$