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Question:

Let z1 and z2 be two complex numbers satisfying |z1| = 9 and |z2 - (3+4i)| = 4. Then the minimum value of |z1 - z2| is:

1

2

0

√2

Solution:

|z1|=9, |z2-(3+4i)|=4
C1(0,0) radius r1=9
C2(3,4) radius r2=4
C1C2=|r1-r2|=5
∴ circle touches internally
∴ |z1-z2|min=0