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$)$

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

Answer 1

The correct option is B $\frac{\left|a\right|}{2}$

The closest distance $=$ length of the perpendicular from the origin on the line $a\overline{z}+\overline{a}z+a\overline{a}=0$

$=\frac{a\left(0\right)+\overline{a}\left|0\right|+a\overline{a}}{2\left|a\right|}$

$=\frac{{\left|a\right|}^2}{2\left|a\right|}$

$=\frac{\left|a\right|}{2}$