Article ID: CBB986120792

On the Development of a Complex Number Interpretation from the 16th to the End of the 19th century (2023)

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We will look at the development of geometric concepts of complex and negative numbers during the period from the 16th to the 20th century. For a long time, these numbers, being obtained analytically, could not find their interpretation; they were called false and imaginary. In 1544, M. Stifel expressed the idea that negative numbers are numbers less than zero. It was a seditious thought because zero meant “nothing” and there could be nothing less than “nothing.” At the turn of the 16th and 17th centuries, this interpretation of negative numbers was embodied in chronology (countdown, before and after the birth of Christ), and in the 18th century, it began to be used in the temperature scale. Attempts at a geometric interpretation of imaginary numbers were undertaken by J. Wallis, G. Leibniz, I. Bernoulli, A. Moivre. L. Euler advanced further than others, who began to depict complex numbers as points on a plane, introduced trigonometric and exponential forms, almost simultaneously with d’Alembert introduced the condition for the analyticity of a function, noticed the symmetry of the function of the conjugate argument, introduced the symbol of an imaginary number. K. Wessel, K. Gauss, and then Argand introduced the complex plane and the geometric interpretation of complex numbers as directed segments, and operations on them. This led W. Hamilton to the concept of quaternion, and his followers to the creation of vector calculus. How much easier the presentation of physics, geodesy, theory of electrical networks, and other applications thanks to complex numbers and vectors!

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Authors & Contributors
Beeley, Philip
Bergmans, Luc
Borgato, Maria Teresa
Bruno, Giuseppe
Demidov, Serghei S.
Euler, Leonhard
Journals
Bollettino di Storia delle Scienze Matematiche
British Society for the History of Mathematics Bulletin
Acta Baltica historiae et philosophiae scientiarum
Almagest
Centaurus: International Magazine of the History of Mathematics, Science, and Technology
Historia Scientiarum: International Journal of the History of Science Society of Japan
Publishers
Birkhäuser
Elsevier
Oxford University Press
Presses Universitaires de Nancy
Princeton University Press
Concepts
Mathematics
Correspondence and corresponding
Science and society
Complex numbers
Mathematicians
Biographies
People
Euler, Leonhard
Alembert, Jean le Rond d'
Hamilton, William Rowan
Lagrange, Joseph Louis
Clairaut, Alexis Claude
Condorcet, Jean Antoine Nicolas Caritat, Marquis de
Time Periods
18th century
19th century
17th century
Early modern
Ancient
Medieval
Places
Great Britain
Berlin (Germany)
Ireland
China
France
Germany
Institutions
Deutsche Akademie der Wissenschaften, Berlin
Oxford University
Royal Society of London
Rossiiskaia Akademiia Nauk
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