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Question

Let z1 and z2 be two complex numbers satisfying |z1|=9 and |z234i|=4. Then the minimum value of |z1z2| is :

A
0
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B
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C
2
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D
2
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Solution

The correct option is A 0
|z1|=9 is a circle with centre C1(0,0) and radius r1=9.
|z234i|=4 is a circle with centre C2(3,4) and radius r2=4.

C1C2=5
|r1r2|=5
C1C2=|r1r2|
Circles touch internally.
|z1z2|min=0

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