Dimination: A Dual Operation to Multiplication and a Geometric Reinterpretation of Complex Numbers
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2026
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| _version_ | 1866901268975321088 |
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| author | Kureshi, Sufiyan |
| author_facet | Kureshi, Sufiyan |
| contents | <p>We introduce dimination, a binary operation defined as repeated subtraction, stand-<br>ing in the same relationship to subtraction as multiplication stands to addition. We<br>show that this operation, combined with a two-axis geometric notation, provides a<br>more intuitive and logically transparent foundation for complex numbers — replacing<br>the historically confusing imaginary unit i with a natural coordinate system of two<br>perpendicular axes, each governed by its own operation pair. We verify that this rein-<br>terpretation is mathematically equivalent to standard complex arithmetic across all<br>major applications, while offering improved pedagogical clarity. The conjugate oper-<br>ation, rotation, Euler’s formula, division, and signal processing all emerge naturally<br>from this framework without appeal to imaginary quantities.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19338512 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Dimination: A Dual Operation to Multiplication and a Geometric Reinterpretation of Complex Numbers Kureshi, Sufiyan <p>We introduce dimination, a binary operation defined as repeated subtraction, stand-<br>ing in the same relationship to subtraction as multiplication stands to addition. We<br>show that this operation, combined with a two-axis geometric notation, provides a<br>more intuitive and logically transparent foundation for complex numbers — replacing<br>the historically confusing imaginary unit i with a natural coordinate system of two<br>perpendicular axes, each governed by its own operation pair. We verify that this rein-<br>terpretation is mathematically equivalent to standard complex arithmetic across all<br>major applications, while offering improved pedagogical clarity. The conjugate oper-<br>ation, rotation, Euler’s formula, division, and signal processing all emerge naturally<br>from this framework without appeal to imaginary quantities.</p> |
| title | Dimination: A Dual Operation to Multiplication and a Geometric Reinterpretation of Complex Numbers |
| url | https://doi.org/10.5281/zenodo.19338512 |