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MATH / Let z₁ and z₂ be complex numbers such that (z₂)/(z₁) is pure imaginary and 2z₁≠7z₂. Compute |(2z₁+7z₂)/(2z₁−7z₂)|.

Problem

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problem

Let z1z_1 and z2z_2 be complex numbers such that z2z1\frac{z_2}{z_1} is pure imaginary and 2z1≠7z2.2z_1 \neq 7z_2. Compute |2z1+7z22z1−7z2|.\left| \frac{2z_1 + 7z_2}{2z_1 - 7z_2} \right|.
Plain-text mathematical notation (without MathML)
Let z₁ and z₂ be complex numbers such that (z₂)/(z₁) is pure imaginary and 2z₁≠7z₂.  Compute
|(2z₁+7z₂)/(2z₁−7z₂)|.
Original LaTeX notation
Let $z_1$ and $z_2$ be complex numbers such that $\frac{z_2}{z_1}$ is pure imaginary and $2z_1 \neq 7z_2.$  Compute
\[\left| \frac{2z_1 + 7z_2}{2z_1 - 7z_2} \right|.\]

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
0f81b203-82a7-52f9-9717-43caab0ace36
task_key
intermediate~5falgebra--test--0f81b203-82a7-52f9-9717-43caab0ace36
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import