Question

If $|z-3+2i|=4,$ then the difference between the greatest value and the least value of $|z|$ is :

• A. $2\sqrt{13}$
• B. $4+\sqrt{13}$
• C. $\sqrt{13}$
• D. $8$

Answer 1

The correct option is A $2\sqrt{13}$

$|z-3+2i|=4$ represents circle with centre $(3,-2)$ and radius is $4$ unit.


Least value of $|z|:$
$|z{|}_{min}=OA=AC-OC$
$=4-\sqrt{3^2+2^2}$
$=4-\sqrt{13}$

Greatest value of $|z|:$
$|z{|}_{max}=OB=BC+OC$
$=4+\sqrt{3^2+2^2}$
$=4+\sqrt{13}$

$\therefore |z{|}_{max}-|z{|}_{min}=2\sqrt{13}$