Open AccessA geometric interpretation of the multiplication of complex numbers
Author(s) -
Luisa Ferro,
J. G. Triana,
S. M. Mendoza
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1674/1/012005
Subject(s) - multiplication (music) , interpretation (philosophy) , complex plane , subtraction , visualization , mathematical proof , computer science , mathematics , arithmetic , algebra over a field , pure mathematics , geometry , artificial intelligence , combinatorics , mathematical analysis , programming language
In complex analysis courses, it is common to use physical interpretations as a didactic tool for teaching complex numbers. In the case of operations between complex numbers, the geometric interpretation of addition and subtraction is well known; however, many authors avoid the interpretation of the multiplication of complex numbers. In this paper, using the physical concepts of rotation and scaling, we will explain the multiplication of complex numbers through visualization in the Argand plane. In addition, we use visual representations in order to obtain proofs without words for some identities.