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  4. If |z+4| ≤ 3, then maximum value of |z+1| is

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Q. If $|z+4| \leq 3$, then maximum value of $|z+1|$ is

Complex Numbers and Quadratic Equations

Solution:

$|z+4| \leq 3$ represents the interior and boundary of the circle with center at -4 and radius equal to 3 . As -1 is an end point of a diameter of the circle, maximum possible value of $|z+1|$ is 6 which is attained when $z=-7$. See Fig. 2.48

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