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If |z1| = 1, |z2| = 2, |z3| = 3 and |9 z1z2 + 4z1z3 + z3z2| = 12 then the value of |z1 + z2 + z3| is equal to

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If |z1| = 1, |z2| = 2, |z3| = 3 and |9 z1z2 + 4 z1z3 + z3z2| = 12 then the value of |z1 + z2 + z3| is equal to

(1) 2 

(2) 3 

(3)4 

(4) 6 

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1 Answer

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Best answer

Correct option is (1) 2

z1 z1 bar = 1, z2 z2 bar = 4, z3z3 bar = 9,

|z1z2z3z3 bar + z2z2 bar z1z3 + z1z1 bar z3z2| = 12

|z1z2z3||z1 bar + z2 bar + z3 bar| = 12

6|z1 + z2 + z3| = 12

|z1 + z2 + z3| = 2

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