Question

If the complex number $z$ satisfies the condition $|z-\frac{12}{z}|=11$, then the maximum distance from origin to point representing $z$ in argand plane is-

• A. $12$
• B. $11$
• C. $17$
• D. $19$

Answer 1

The correct option is A $12$

$|z-\frac{12}{z}|=11\Rightarrow |z^2-12|=11|z|$
$\Rightarrow {\left|z\right|}^2-11\left|z\right|-12\le 0\Rightarrow (\left|z\right|+1)(\left|z\right|-12)\le 0$
$-1\le \left|z\right|\le 12$ $\Rightarrow$ $0\le \left|z\right|\le 12$
$\Rightarrow$ $|z-0|\le 12$
$\Rightarrow$ The maximum distance of $z$ from origin is $12$