If $z$ is any complex number satisfying $|z-3-2 i| \leq 2$, then the minimum value of $|2 z-6+5 i|$

Question

If $z$ is any complex number satisfying $|z-3-2 i| \leq 2$, then the minimum value of $|2 z-6+5 i|$ is

Professor PC Thomas Classes · Answer

(5) : $|2 z-6+5 i|$\ $=2\left|z-\left(3-\frac{5}{2} iight)ight|$\ Min. distance\ $=\left(2+\frac{5}{2}ight)-2=\frac{5}{2}$\ Hence $2\left|z-\left(3-\frac{5}{2} iight)ight|_{	ext {min. }}=2 \cdot \frac{5}{2}=5$\