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Question

For all complex numbers z1,z2 satisfying |z1|=12 and |z2(3+4i)|=5, the minimum value of |z1z2| is

A
4
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B
3
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C
1
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D
2
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Solution

The correct option is D 2
The two circles whose centre and radius are C1(0,0),r1=12,C2(3,4),r2=5 and it passes through origin ie, the centre of C1.
Now, C1C2=32+42=5
and r1r2=125=7
C1C2<r1r2
Hence, circle C2 lies inside the circle C1.
From figure the, minimum distance between them is
AB=C1BC1A=r12r2
=1210=2

507243_473608_ans_b175cbb3625542b0bb1af9bae6ef5681.png

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