# If $\mid z+4\mid\leq 3$,then maximum value of $\mid z+1\mid$ is

$\begin{array}{1 1}(A) 4 \\ (B) 10 \\ (C) 6 \\(D) 0 \end{array}$

$\mid z+4\mid\leq 3$ 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 $z=-7$
$\Rightarrow \mid Z+1\mid=6$
Hence (C) is the correct answer.