Q. If $\left|z+4\right|\le3$, then the maximum value of $|z + 1|$ is
AIEEEAIEEE 2007Complex Numbers and Quadratic Equations
Solution:
From the Argand diagram maximum
value of $|z + 1|$ is 6.
Alternative:
$|z + 1| = |z + 4 − 3|$
$\le|z + 4| + |−3| = 6.$
