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Question

For all complex numbers z1,z2 satisfying |z1|=12 and |z234i|=5, the minimum value of |z1z2| 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 C 2
Ans.(b). The two circles are C1(0,0), r1=12
C2(3,4), r2=5
and it passes through origin, the center of C1.
C1C2=5<r1r2=7
Hence circle C2 lies inside circle C1.
Therefore minimum distance between them is
AB=C1BC1Ar12r2=1210=2
1107534_999523_ans_1e33d78d61254abc968aa1c020ee2266.png

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