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MATH / Let z₁, z₂, z₃ be complex numbers such that |z₁|=1, |z₂|=2, |z₃|=3, and |9z₁z₂+4z₁z₃+z₂z₃|=12.Find |z₁+z₂+z₃|.

Problem

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problem

Let z1,z_1, z2,z_2, z3z_3 be complex numbers such that |z1|=1,|z_1| = 1, |z2|=2,|z_2| = 2, |z3|=3,|z_3| = 3, and |9z1z2+4z1z3+z2z3|=12.|9z_1 z_2 + 4z_1 z_3 + z_2 z_3| = 12.Find |z1+z2+z3|.|z_1 + z_2 + z_3|.
Plain-text mathematical notation (without MathML)
Let z₁, z₂, z₃ be complex numbers such that |z₁|=1, |z₂|=2, |z₃|=3, and
|9z₁z₂+4z₁z₃+z₂z₃|=12.Find |z₁+z₂+z₃|.
Original LaTeX notation
Let $z_1,$ $z_2,$ $z_3$ be complex numbers such that $|z_1| = 1,$ $|z_2| = 2,$ $|z_3| = 3,$ and
\[|9z_1 z_2 + 4z_1 z_3 + z_2 z_3| = 12.\]Find $|z_1 + z_2 + z_3|.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
d7e6a81b-605f-5aec-af0d-e1ac4ebe007c
task_key
intermediate~5falgebra--test--d7e6a81b-605f-5aec-af0d-e1ac4ebe007c
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import