Question

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

• A. $1$ unit
• B. $\frac{Re\left(a\right)}{|a|}$
• C. $\frac{I_m\left(a\right)}{|a|}$
• D. $\frac{|a|}{2}$

Answer 1

The correct option is D $\frac{|a|}{2}$

Given curve
$a\overline{z}+\overline{a}z+a\overline{a}=0$
which is a straight line
${\perp }^r$ distance from origin
$\left|\frac{a\left(0\right)+\overline{a}\left(0\right)+a\overline{a}}{2\left|a\right|}\right|$
=$\frac{{\left|a\right|}^2}{2\left|a\right|}=\frac{\left|a\right|}{2}$