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Question

|z1|=1,|z2|=2,|z3|=3and|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|=1,z1¯¯¯¯¯z1=1|z2|=2,z2¯¯¯¯¯z2=4|z3|=3,z3¯¯¯¯¯z3=9|9z1z2+4z1z3+z2z3|=12z1z2z3¯¯¯¯¯z3+z1z2z3¯¯¯¯¯z2+z1¯¯¯¯¯z1z2z3=12|z1z2z3|¯¯¯¯¯z1+¯¯¯¯¯z2+¯¯¯¯¯z3=12|z1||z2||z3|¯¯¯¯¯z1+¯¯¯¯¯z2+¯¯¯¯¯z3=126¯¯¯¯¯z1+¯¯¯¯¯z2+¯¯¯¯¯z3=12¯¯¯¯¯z1+¯¯¯¯¯z2+¯¯¯¯¯z3=2|z1+z2+z3|=2


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