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 A2 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