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Question

For all complex numbers z1,z2 satisfying |z1|=12;|z2−3−4i|=5, the minimum value of |z1−z2| is

A
0
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B
2
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C
7
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D
17
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Solution

The correct option is B 2
The two circles are C1(0,0),r1=12;C2(3,4),r2=5 and it passes through origin.
The distance between centres is C1C2=32+42<7=r1r2
Hence, circle C2 lies inside circle C1.
Therefore, the minimum distance between them is
AB=C1BC1A=r12r2=1210=2

723801_684538_ans_eacbe3ec84c84f4ba238183066a92019.png

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