If z is a complex number satisfying |z - 3| l | vedclass

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(C) The condition $|z - 3| \leq 5$ represents a disk in the complex plane centered at $C = (3, 0)$ with radius $R = 5$.We want to find the range of $|

Vedclass · Accepted Answer

$[0, 5 + 3\sqrt{2}]$

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(C) The condition $|z - 3| \leq 5$ represents a disk in the complex plane centered at $C = (3, 0)$ with radius $R = 5$.We want to find the range of $|z - (-3i)|$,which represents the distance of points $z$ in the disk from the point $P = (0, -3)$.The distance between the center $C(3, 0)$ and the point $P(0, -3)$ is $d = \sqrt{(3 - 0)^2 + (0 - (-3))^2} = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$.The minimum distance from $P$ to the disk is $\max(0, d - R) = \max(0, 3\sqrt{2} - 5) = 0$ (since $3\sqrt{2} \approx 4.24 The maximum distance from $P$ to the disk is $d + R = 3\sqrt{2} + 5$.Thus,the range of $|z + 3i|$ is $[0, 5 + 3\sqrt{2}]$.

If $z$ is a complex number satisfying $|z - 3| \leq 5$,then the range of $|z + 3i|$ is (where $i = \sqrt{-1}$)

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