Question

If $z$ is a complex number such that $|z-3+2i|=4$ and $m,M$ are the minimum and maximum values of $|z|$ respectively, then the value of $m^2+M^2$ is equal to

• A. $56$
• B. $58$
• C. $60$
• D. $64$

Answer 1

The correct option is B $58$

$|z-(3-2i)|=4$ represents a circle with centre $C(-3,2)$ and radius, $r=4$
Let $O$ be the origin.
$|z{|}_{min}=r-OC=4-\sqrt{13}$
$|z{|}_{max}=r+OC=4+\sqrt{13}$
$\therefore m^2+M^2=(4-\sqrt{13}{)}^2+(4+\sqrt{13}{)}^2=58$