Question

For all complex numbers $z_1,z_2$ satisfying $\left|z_1\right|=12$ and $|z_2-3-4i|=5,$ the minimum value of $|z_1-z_2|$ is

• A. $0$
• B. $2$
• C. $7$
• D. $17$

Answer 1

The correct option is B $2$

The first is a circle with center at $(0,0)$ and radius $12$.
The second is a circle with center at $(3,4)$ and radius $5$ which passes through the origin (since $\sqrt{3^2+4^2}=5$)
The minimum value can be seen from the diagram as $2$.
Hence, (b) is correct.