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Question

If |z1|=1,|z2|=2,|z3|=3 and |9z1z2+4z1z3+z2z3|=12, then the value of |z1+z2+z3| is equal to

A
2
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B
3
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C
4
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D
6
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Solution

The correct option is A 2
z1¯z1=1, z2¯z2=4, z3¯z3=9
Given |9z1z2+4z1z3+z2z3|=12
|z3¯z3z1z2+z2¯z2z1z3+z1¯z1z2z3|=12
|z1||z2||z3||¯z1+¯z2+¯z3|=12
6|z1+z2+z3|=12 (|¯z1+¯z2+¯z3|=|z1+z2+z3|)
|z1+z2+z3|=2

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