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Question

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

A
\N
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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
|z1z2|=|z1(z234i)(3+4i)||z1||z234i||3+4i|1255 [using |z1z2||z1||z2|]
Alternate Solution
Clearly from the figure |z1z2| is minimum when z1,z2 lie along the diameter.

|z1z2|C2BC2A|z1z2|1210=2

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