A interpretação geométrica dos números imaginários no século XIX : a contribuição de Jean Robert Argand (1768-1822)

Abstract

From the Middle Ages onwards, when algebra entered into a more intense development, the problem of the square roots of negative numbers, which inevitably appeared in the process of the resolution of algebraic equations bothered people. Clearly, if we identify numbers with quantities it doesn't make sense to speak of such roots and even of negative numbers. Numbers of that type were thus called impossible numbers, absurdities, false or imaginary, names that express the confusion they caused in mathematics. On the other hand such symbols were well defined in terms of operation and as mathematics up to the 19th century was mainly conceived in algorithmic or constructive terms these numbers were used as part of the calculation. Only in the turning of the century XVIII for the XIX, when a new view of mathematics began to evolve based on new types of applications on searched for a reference of these symbols and found it in the different geometric representations for those numbers, what guaranteed their full acceptance within the universe of the numbers and clarified their place in the overall realm of numbers.. One of the main contributors to the solution of the problem was the Swiss librarian Jean Robert Argand (1768-1822), who in 1806 published, in Annales of Mathématiques of Gergonne, the Rehearsal on a way of representing the imaginary amounts in the geometric constructions. In spite of its importance, that work only became known in 1813.