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In mathematics, an ''n''th-order '''Argand system''' (named after {{wipe|France}} [[Biography:Mathematician|mathematician]] [[Biography:Jean-Robert Argand|Jean-Robert Argand]]) is a [[Coordinate system|coordinate system]] constructed around the ''n''th [[Root of unity|roots of unity]]. From the [[Origin (mathematics)|origin]], ''n'' axes extend such that the angle between each axis and the axes immediately before and after it is 360/''n'' [[Degree (angle)|degrees]]. For example, the [[Number line|number line]] is the 2nd-order Argand system because the two axes extending from the origin represent 1 and&nbsp;−1, the 2nd roots of unity. The [[Complex plane|complex plane]] (sometimes called the Argand plane, also named after Argand) is the 4th-order Argand system because the 4 axes extending from the origin represent 1, ''i'', −1, and −''i'', the 4th roots of unity.

==References==
*Flanigan, Francis J., ''[https://archive.org/details/complexvariables00flan/page/n5/mode/2up Complex Variables: Harmonic and Analytic Functions]'', Dover, 1983, {{isbn|0-486-61388-7}}
* Jones, Phillip S., "Argand, Jean-Robert", ''Dictionary of Scientific Biography'' 237&ndash;240, Charles Scribner's Sons, 1970, {{isbn|0-684-10114-9}}

[[Category:Mathematical structures]]



{{Sourceattribution|Argand system}}