The closest distance of the origin from a curve given as $a\bar z + \bar az + a\bar a = 0$ ($a$ is a complex number) is.
• A
$1$
• A
$1$
• B
$\dfrac {Re(|a|)}{|a|}$
• B
$\dfrac {Re(|a|)}{|a|}$
• C
$\dfrac {Im(|a|)}{|a|}$
• C
$\dfrac {Im(|a|)}{|a|}$
• D
$\dfrac {|a|}{2}$
• D
$\dfrac {|a|}{2}$

#### Solution

The closest distance $=$ length of perpendicular from the origin on the line $a\bar z + \bar az + a\bar a = 0$

$\begin{array}{l} =\frac { { a\left( 0 \right) +\bar { a } \left| 0 \right| +a\bar { a } } }{ { 2\left| a \right| } } \\ =\frac { { { { \left| a \right| }^{ 2 } } } }{ { 2\left| a \right| } } \\ =\frac { { \left| a \right| } }{ 2 } \end{array}$

Hence, Option $D$ is the correct answer.