Question

If $|z+4|\le 3$, then greatest & least values of |z + 1| are

• A. 4, 1
• B. 6, 0
• C. 6, 1
• D. 4, 0

Answer 1

The correct option is B 6, 0

$\mid z+4\mid \le 3$ represents points inside and on boundary of circle with centre $-4$ and radius $3$

From figure it is clear that maximum value of $\mid z+1\mid$ will be obtained at $z=-7$

$\Rightarrow$ $\mid Z+1\mid =|-7+1|=|-6|=6$

From figure it is clear that maximum value of $\mid z+1\mid$ will be obtained at $z=-1$

$\Rightarrow$ $\mid Z+1\mid =|-1+1|=|0|=0$

$\therefore$ The greatest and least values of $|z+1|$ are $6$ and $0.$