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Question

For all complex numbers z1,z2 satisfying |z1|=12 and |z234i|=5, then 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 B 2
Given:-
z1 and z2 are the complex number.
|z1|=12|z234i|=5
To find minimum value of |z1z2|
Solution:-
We know that
|z1z2||z1||z2|
and
|z234i||z2||3+4i|
|z234i||z2|(3)2+(4)2{|a+bi|}=a2+b25|z2|5|z2|10
for minimum value.z2=10
minimum value of |z1z2||z1||z2||z1z2|1210|z1z2|2
Hence the minimum value of |z1||z2|=2

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