Jean robert argand biography of christopher

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Argand recognized the nonrigorous nature of his reasoning, but he defined his goals as clarifying thinking about imaginaries by setting up a new view of them and providing a new tool for research in geometry.

Argand’s notation in his original essay is of particular interest because it anticipated the more abstract and modern ideas, later expounded by W.

R. Hamilton, of complex numbers as arbitrarily constructed new entities defined as ordered pairs of real numbers. However, the fact that his name is associated with this geometrical interpretation of complex numbers is only as a result of a rather strange sequence of events.

Here is a sketch of this work that you may be interested in and that will allow you to judge the rest. He gave a beautiful proof (with small gaps) of the fundamental theorem of algebra in his work of 1806, and again when he published his results in Gergonne's Journal in 1813. The Essay discussed a method of graphing complex numbers via analytical geometry.

It proposed the interpretation of the value i as a rotation of 90 degrees in the Argand plane.

A vigorous discussion between Jacques Français, Argand and Servois took place in the pages of Gergonne's Journal. 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 . Cauchy mentioned Argand twice in his “Mémoire sur les quantités géométriques,” which appeared in Exercices d’analyse et de physique mathématique (1847).

He noted that in them the means have the same or opposite signs, depending upon whether the signs of the extremes are alike or opposite.

The first to publish this geometrical interpretation of complex numbers was Caspar Wessel. His letters and published work all appear under the name Argand with no other names.

One might have expected that Argand would have made no other contributions to mathematics.

On the other hand, Argand - apparently a shy man - abstained from publishing his paper, due to Legendre's uninterested and sceptical reaction. There is nothing like an argument to bring something to the attention of the world and this is exactly what happened next. This led him to consider 1 :x: :x: — 1. The following information about Jean Robert Argand has, probably incorrectly, become a standard part of the biography of the man who invented the 'Argand diagram'.

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.