Let z_1 and z_2 be two complex numbers satisf | vedclass

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(A) Given $|z_1| = 9$,this represents a circle $C_1$ centered at $(0, 0)$ with radius $r_1 = 9$.Given $|z_2 - (3 + 4i)| = 4$,this represents a circle

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(A) Given $|z_1| = 9$,this represents a circle $C_1$ centered at $(0, 0)$ with radius $r_1 = 9$.Given $|z_2 - (3 + 4i)| = 4$,this represents a circle $C_2$ centered at $(3, 4)$ with radius $r_2 = 4$.The distance between the centers $C_1(0, 0)$ and $C_2(3, 4)$ is $d = \sqrt{(3-0)^2 + (4-0)^2} = \sqrt{9 + 16} = 5$.Since the distance between centers $d = 5$ and the difference of radii $|r_1 - r_2| = |9 - 4| = 5$,we have $d = |r_1 - r_2|$.This implies that the circle $C_2$ lies inside the circle $C_1$ and touches it internally.Since the circles touch internally,the minimum distance between any point $z_1$ on $C_1$ and $z_2$ on $C_2$ is $0$.

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

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