Let z_1 and z_2 be two complex numbers satisfying |z_1|=9 and |z_2-3-4i|=4.

Question

Let $z_1$ and $z_2$ be two complex numbers satisfying $|z_1|=9$ and $|z_2-3-4i|=4$. Then the minimum value of $|z_1-z_2|$ is:

Accepted Answer

$z_1$ lies on a circle of radius 9 about the origin; $z_2$ lies on a circle of radius 4 about $(3,4)$ (distance $5$ from origin). Since $5+4=9$, the two circles touch, so the minimum value is 0.

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