Jean-Robert Argand
Encyclopedia
Jean-Robert Argand was a gifted 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
.
, Switzerland
to Jacques Argand, his father, and Eve Carnac, his mother. 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 numbers, as well as the notation for vectors
. 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 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 polynomials with complex coefficients. In 1978 it was called by The Mathematical Intelligencer “both ingenious and profound,” and was later referenced in Cauchy's Cours d’Analyse and Chrystal's
influential textbook Algebra.
Jean-Robert Argand died of an unknown cause on August 13, 1822 in Paris.
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, he published the idea of geometrical interpretation of complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s known as the Argand diagram
Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis...
.
Life
Jean-Robert Argand was born in GenevaGeneva
Geneva In the national languages of Switzerland the city is known as Genf , Ginevra and Genevra is the second-most-populous city in Switzerland and is the most populous city of Romandie, the French-speaking part of Switzerland...
, Switzerland
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
to Jacques Argand, his father, and Eve Carnac, his mother. 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
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
). 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 numbers, as well as the notation for vectors
. The topic of complex numbers was also being studied by other mathematicians, notably Carl Friedrich GaussCarl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
and Caspar Wessel
Caspar Wessel
Caspar Wessel was a Norwegian-Danish mathematician and cartographer. In 1799, Wessel was the first person to describe the complex numbers. He was the younger brother of poet and playwright Johan Herman 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
Fundamental theorem of algebra
The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root...
in his 1814 work Réflexions sur la nouvelle théorie d'analyse (Reflections on the new theory of 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 polynomials with complex coefficients. In 1978 it was called by The Mathematical Intelligencer “both ingenious and profound,” and was later referenced in Cauchy's Cours d’Analyse and Chrystal's
George Chrystal
George Chrystal was a Scottish mathematician.He was born in Old Meldrum and educated at Aberdeen Grammar School and the University of Aberdeen, moving in 1872 to study under James Clerk Maxwell at Peterhouse, Cambridge, where he graduated Second wrangler in 1875, joint with William Burnside, and...
influential textbook Algebra.
Jean-Robert Argand died of an unknown cause on August 13, 1822 in Paris.
See also
- Caspar WesselCaspar WesselCaspar Wessel was a Norwegian-Danish mathematician and cartographer. In 1799, Wessel was the first person to describe the complex numbers. He was the younger brother of poet and playwright Johan Herman Wessel....
- iImaginary unitIn mathematics, the imaginary unit allows the real number system ℝ to be extended to the complex number system ℂ, which in turn provides at least one root for every polynomial . The imaginary unit is denoted by , , or the Greek...
, the imaginary square root of −1 - Complex numberComplex numberA complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
- Complex planeComplex planeIn mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis...
(also known as Argand plane)
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