Question

If $|z+3|\le 3$ then find minimum and maximum values of $|z|$, $|z-1|$, $|z+1|$

Answer 1

$|z+3|\le 3$

$z+3=3+3=-3$

$z=0$

Minimum : $-6$

Maximum : $0$

Maximum value of $|z|=6$

Minimum value of $|z|=0$

Maximum value of $|z-1|=7$

Minimum value of $|z-1|=1$

Maximum value of $|z+1|=5$

Minimum value of $|z+1|=1$