JEE Main · 2007 · 29 Apr 2007 · Offline · Complex Numbers

The condition $|z+4|\le 3$ describes a disc centred at $-4$ with radius $3$. Writing $z+1=(z+4)-3$ and using the triangle inequality, $|z+1|\le |z+4|+3\le 3+3=6$. The greatest value $6$ is attained at the boundary point farthest from $-1$, namely $z=-7$.