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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 B 2

Circle 1:|z1|=12
If we consider Circle 1 then center is at (0,0) and radius is 12 units
Circle 2:|z234i|=5
If we consider Circle 2 then center is at (3,4) and radius is 5 units
From the fig.
min|z1z2| will be the black colored mark in the image ie.Radius of Circle1Diameter of Circle2
min |z1z2|=1210=2


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