Question

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

Options

• 3

• 4

• 8

• 2

Answer 1

2

Explanation:

|z₁| = 1, |z₂| = 2, |z₃| = 3

`=> "z"_1bar"z"_1 = 1, "z"_2bar"z"_2 = 4, "z"_3bar"z"_3 = 9`

|9z₁z₂ + 4z₁z₃ + z₂z₃| = 12

`=> |"z"_3  bar"z"_3  "z"_1 "z"_2 + "z"_2  bar"z"_2 "z"_1 "z"_3 + "z"_1  bar"z"_1 "z"_2 "z"_3|` = 12

`=> |"z"_1 "z"_2 + "z"_3| |bar"z"_3 + bar"z"_2 + bar"z"_1|` = 12

⇒ |z₁ + z₂ + z₃| = 2