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  4. If |z1| = 2, |z2| = 3 then |z1 + z2 + 5 + 12i| is less than or equal to

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Q. If $|z_1| = 2, |z_2| = 3$ then $|z_1 + z_2 + 5 + 12i|$ is less than or equal to

Complex Numbers and Quadratic Equations

Solution:

$\because |z_1 + z_2 + ... + z_n| \le |z_1| + |z_2| + ... + |z_n|$
$\therefore |z_1 + z_2 + (5 + 12 i)| \le |z_1| + |z_2| + |5 + 12i|$
$= 2 + 3 + 13 = 18$