argument

Angle of complex number about real axis

Also known as argument of a complex number · complex argument · arg · arg(z)

Instance of: multivalued function

Overview

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In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in Figure 1. By convention the positive real axis is drawn pointing rightward, the positive imaginary axis is drawn pointing upward, and complex numbers with positive real part are considered to have an anticlockwise argument with positive sign.

Overview

All data

18 statements · 11% with external sources · numbers in brackets are citations

Partial function domain: set of complex numbers
Codomain: set of real numbers
Different from: argument of a function
complex sign function
arg max and min
Image of function: set of real numbers applies to part: multivalued function
Upper open interval between 0 and 2π applies to part: principal branch
Defining formula: \varphi = \arg(r \mathrm{e}^{\mathrm{i} \varphi}), -\pi < \varphi \leq \pi
In defining formula: \arg z symbol represents: argument
\mathrm{e} symbol represents: Euler's number
\mathrm{i} symbol represents: imaginary unit
r symbol represents: real number

On other databases

6 identifiers linking argument across the web's reference databases

Data quality

statements

11%

externally sourced

Source last edited August 3, 2026. AIDB refreshes this page daily.

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AIDB. (2026). argument (Q1780131). Retrieved from https://aidb.si/e/argument-Q1780131