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MATH / Find the number of pairs (z₁,z₂) of complex numbers such that:

Problem

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problem

Find the number of pairs (z1,z2)(z_1,z_2) of complex numbers such that: z1z2z_1 z_2 is pure imaginary z1z2\frac{z_1}{z_2} is real |z1|=|z2|=1.|z_1| = |z_2| = 1.
Plain-text mathematical notation (without MathML)
Find the number of pairs (z₁,z₂) of complex numbers such that:

z₁z₂ is pure imaginary
(z₁)/(z₂) is real
|z₁|=|z₂|=1.
Original LaTeX notation
Find the number of pairs $(z_1,z_2)$ of complex numbers such that:

$z_1 z_2$ is pure imaginary
$\frac{z_1}{z_2}$ is real
$|z_1| = |z_2| = 1.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
ff81762a-2ef5-5bbf-9877-d329d534e930
task_key
intermediate~5falgebra--test--ff81762a-2ef5-5bbf-9877-d329d534e930
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import