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

Question

Aicharya · Accepted Answer

Given, $|z-3-2 i| \leq 2$ To find minimum of $|2 z-6+5 i|$ or $\quad 2\left|z-3+\frac{5}{2} iight|$ Using triangle inequality, i.e. ||$z_1|-| z_2|| \leq\left|z_1+z_2ight|$ $	herefore\left|z-3+\frac{5}{2} iight|$ $=\left|z-3-2 i+2 i+\frac{5}{2} iight|$ $=\left|(z-3-2 i)+\frac{9}{2} iight| \geq|| z-3-2 i\left|-\frac{9}{2}ight|$ $\geq\left|2-\frac{9}{2}ight| \geq \frac{5}{2} \Rightarrow\left|z-3+\frac{5}{2} iight| \geq \frac{5}{2}$ or $\quad|2 z-6+5 i| \geq 5$

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

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