Jean-Robert Argand
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Jean-Robert Argand (, , ; July 18, 1768 – August 13, 1822) was a Genevan amateur mathematician. In 1806, while managing a
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in
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, he published the idea of geometrical interpretation of
complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...
s known as the Argand diagram and is known for the first rigorous
proof Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a co ...
of the
Fundamental Theorem of Algebra The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant polynomial, constant single-variable polynomial with Complex number, complex coefficients has at least one comp ...
.


Life

Jean-Robert Argand was born in
Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...
, then
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, 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 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 as a rotation of 90 degrees in the Argand plane. In this essay he was also the first to propose the idea of modulus to indicate the magnitude of vectors and
complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...
s, as well as the notation for vectors \overrightarrow. The topic of complex numbers was also being studied by other mathematicians, notably
Carl Friedrich Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and ...
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 The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant polynomial, constant single-variable polynomial with Complex number, complex coefficients has at least one comp ...
in his 1814 work ''Réflexions sur la nouvelle théorie d'analyse'' (Reflections on the new theory of
analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
). 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 In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ...
s with complex
coefficient In mathematics, a coefficient is a Factor (arithmetic), multiplicative factor involved in some Summand, term of a polynomial, a series (mathematics), series, or any other type of expression (mathematics), expression. It may be a Dimensionless qu ...
s. The first textbook containing a proof of the theorem was
Cauchy Baron Augustin-Louis Cauchy ( , , ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real a ...
's '' 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 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 * ''i'', the imaginary square root of
−1 In mathematics, −1 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than  0. ...
*
Complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...
*
Complex plane In mathematics, the complex plane is the plane (geometry), plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, call ...
(also known as Argand plane)


References

* 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

*


External links

* * Robert Argand, ''Essai sur une manière de représenter des quantités imaginaires dans les constructions géométriques'', 2e édition, Gauthier Villars, Paris (1874
BNF

Jean-Robert Argand, Biography on ''s9.com''

Imaginary quantities; their geometrical interpretation
English translation of Jean-Robert Argand's original French work {{DEFAULTSORT:Argand, Jean-Robert 1768 births 1822 deaths 18th-century mathematicians from the Republic of Geneva Amateur mathematicians 19th-century Swiss mathematicians Complex numbers