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Argand diagram (Definition)

An Argand diagram is the graphical representation of complex numbers written in polar coordinates. For example, if $z\in \mathbb{C}$ is a complex number, then $z$ can be written as $re^{i\theta}$ , where $r$ is the length of $z$ considered as a vector $(x,y)\in \mathbb{R}^2$ , with $z=x+yi$ , and $\theta$ is the value such that $\tan \theta = \frac{y}{x}$ , and can be interpreted as the angle $z$ makes with the $x$ -axis. The Argand diagram of $z$ is thus


\begin{pspicture}(-0.5,-0.5)(4.5,2) \SpecialCoor \psline{->}(0,0)(4.5,0) \rput(4... ...0){1}{0}{(3,1.75)} \rput(1.25,0.3){$\theta$} \rput(1.5,1.2){$r$} \end{pspicture}

Argand is the name of Jean-Robert Argand, the Frenchman who is credited with the geometric interpretation of the complex numbers [Biography]




"Argand diagram" is owned by CWoo. [ full author list (3) | owner history (3) ]
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See Also: complex

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Cross-references: interpretation, angle, vector, length, polar coordinates, complex numbers, representation
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This is version 6 of Argand diagram, born on 2001-11-11, modified 2008-02-07.
Object id is 751, canonical name is ArgandDiagram.
Accessed 9770 times total.

Classification:
AMS MSC28A10 (Measure and integration :: Classical measure theory :: Real- or complex-valued set functions)
 30-00 (Functions of a complex variable :: General reference works )

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