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Question

For all complex numbers z1 and z2 satisfying |z1|=12 and |z234i|=5, the minimum value of |z1z2| is

A
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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 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

Then we have
C1C2=(x2x1)2+(y2y1)2=32+42=5

and r1r2=125=7

C1C2<r1r2

Hence, circle C2 lies inside circle C1

Now, the minimum distance between them is

AB=C1BC1A=r12r2=1210=2

|z1z2|=2

724004_680964_ans_2053f38ad89f467a883191949e371027.png

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