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{{Short description|Genevan mathematician}}
{{Infobox scientist
|name              = Jean-Robert Argand
|caption           = Jean-Robert Argand
|birth_date        = July 18, 1768
|birth_place       = [[Geneva]], Republic of Geneva
|death_date        = {{D-da|August 13, 1822|July 18, 1768}}
|death_place       = [[Paris]] 
|residence         = 
|citizenship       = 
|nationality       = Republic of Geneva, and then [[Switzerland]] (since 1815)
|ethnicity         = 
|field             = [[Mathematics]]
|work_institutions = 
|alma_mater        = 
|doctoral_advisor  = 
|doctoral_students = 
|known_for         = [[Argand diagram]] and Proof of [[Fundamental Theorem of Algebra]]
|author_abbrev_bot = 
|author_abbrev_zoo = 
|influences        = 
|influenced        = 
|prizes            = 
|religion          = 
|footnotes         = 
|signature         =
}}'''Jean-Robert Argand''' ({{IPAc-en|UK|ˈ|ɑːr|ɡ|æ|n|d}}, {{IPAc-en|US|ˌ|ɑːr|ˈ|ɡ|ɑː|n|(|d|)}},<ref>{{cite LPD|3}}</ref><ref>{{cite EPD|18}}</ref> {{IPA|fr|ʒɑ̃ ʁɔbɛʁ aʁɡɑ̃|lang}}; July 18, 1768 – August 13, 1822) was a Genevan [[List of amateur mathematicians|amateur mathematician]]. In 1806, while managing a [[bookstore]] in [[Paris]], he published the idea of geometrical interpretation of [[complex number]]s known as the [[Argand diagram]] and is known for the first rigorous [[mathematical proof|proof]] of the [[Fundamental Theorem of Algebra]].

==Life==

Jean-Robert Argand was born in [[Geneva]], then [[Republic of Geneva]], to Jacques Argand and Eve Carnac.  His background and education are mostly unknown.  Since his knowledge of mathematics was self-taught and he did not belong to any mathematical organizations, he likely pursued mathematics as a hobby rather than a profession.

Argand moved to Paris in 1806 with his family and, when managing a bookshop there, privately published his ''Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques'' (Essay on a method of representing [[complex number|imaginary quantities]]). In 1813, it was republished in the French journal ''Annales de Mathématiques''. The Essay discussed a method of graphing complex numbers via analytical geometry. It proposed the interpretation of the value {{math|''i''}} as a rotation of 90 degrees in the Argand plane. In this essay he was also the first to propose the idea of [[absolute value|modulus]] to indicate the magnitude of [[Euclidean vector|vectors]] and [[complex number]]s, as well as the notation for vectors <math>\overrightarrow{a b}</math>. The topic of complex numbers was also being studied by other mathematicians, notably [[Carl Friedrich Gauss]] and [[Caspar Wessel]].  Wessel's 1799 paper on a similar graphing technique did not attract attention.

Argand is also renowned for delivering a proof of the [[fundamental theorem of algebra]] in his 1814 work ''Réflexions sur la nouvelle théorie d'analyse'' (Reflections on the new theory of [[mathematical analysis|analysis]]). It was the first complete and [[rigorous proof]] of the theorem, and was also the first proof to generalize the fundamental theorem of algebra to include [[polynomial]]s with complex [[coefficient]]s.

The first textbook containing a proof of the theorem was [[Cauchy]]'s ''[[Cours d'Analyse|Cours d'analyse de l'École Royale Polytechnique]]'' (1821). It contained Argand's proof, although Argand is not credited for it. And the proof was later referenced in [[George Chrystal|Chrystal's]] influential textbook ''Algebra''.

Argand died of an unknown cause on August 13, 1822, in Paris. In 1978 his proof of the fundamental theorem of algebra was called by The Mathematical Intelligencer “both ingenious and profound.”

==See also==

* [[Caspar Wessel]]
* [[Imaginary unit|''i'']], the imaginary square root of [[−1 (number)|−1]]
* [[Complex number]]
* [[Complex plane]] (also known as Argand plane)

==References==
{{Reflist}}

* Roy, J. (n.d.) James Robert Argand Biography | World of Mathematics.  ''Bookrags.com.''  Retrieved March 18, 2008.  From http://www.bookrags.com/biography/jean-robert-argand-wom/.
*McGrath, K., Travers B., et al. (n.d.)  James Robert Argand Biography | Word of Scientific Discovery.  ''Bookrags.com.''  Retrieved March 18, 2008.  From http://www.bookrags.com/biography/jean-robert-argand-wsd/.

==Further reading==
* {{cite encyclopedia
  | last = Jones
  | first = Phillip S.
  | title = Argand, Jean Robert
  | encyclopedia = [[Dictionary of Scientific Biography]]
  | volume = 1
  | pages = 237–240 
  | publisher = Charles Scribner's Sons
  | location = New York
  | year = 1970
  | isbn = 0-684-10114-9
 }}

==External links==
* {{MacTutor Biography|id=Argand}}
* Robert Argand, ''Essai sur une manière de représenter des quantités imaginaires dans les constructions géométriques'', 2e édition, Gauthier Villars, Paris (1874) [http://gallica.bnf.fr/ BNF]
* [http://www.s9.com/Biography/Argand-Jean-Robert Jean-Robert Argand, Biography on ''s9.com''] {{Webarchive|url=https://web.archive.org/web/20150916231839/http://www.s9.com/Biography/Argand-Jean-Robert |date=2015-09-16 }}
* [https://archive.org/details/imaginaryquanti00argagoog Imaginary quantities; their geometrical interpretation], English translation of Jean-Robert Argand's original French work

{{Authority control}}

{{DEFAULTSORT:Argand, Jean-Robert}}
[[Category:1768 births]]
[[Category:1822 deaths]]
[[Category:18th-century mathematicians from the Republic of Geneva]]
[[Category:Amateur mathematicians]]
[[Category:19th-century Swiss mathematicians]]
[[Category:Complex numbers]]