The Nature of Imaginary Numbers from the Perspective of their “Dimensionality”

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Year:
2024
Type of Publication:
Article
Keywords:
Imaginary Numbers, N-Dimensional Mathematical Objects, Brahmagupta's Rules, Complex Plan
Authors:
Antonio Luigi Paolilli
Journal:
IJISM
Volume:
12
Number:
1
Pages:
1-4
Month:
January
ISSN:
2347-9051
Abstract:
The aim of this paper is to gain a better understanding of the nature of imaginary numbers, considering them as mathematical objects characterized by a lower dimensionality than that of real numbers. For this purpose, in addition to an article written a few years ago on the dimensional aspect of mathematical objects, reference will be made to the rules of arithmetic presented by Brahmagupta. In particular, it will be emphasized that even the nature of the arithmetic operation of multiplication has been misunderstood with regard to the roots of negative numbers. The negative numbers from which the square root is extracted are not to be seen as the result of a multiplication performed on the real straight line, i.e. without changing the nature of the multiplicand, but as the product between quantities of the same nature, a product that generates mathematical objects characterized by a nature different from that of the multiplicand. An alternative graphic approach to the usual one will finally better clarify the nature of imaginary numbers, highlighting their concreteness.

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