Dimination: A Dual Operation to Multiplication and a Geometric Reinterpretation of Complex Numbers
Year: 2026
Type: preprint
Abstract: We introduce dimination, a binary operation defined as repeated subtraction, stand-ing in the same relationship to subtraction as multiplication stands to addition. Weshow that this operation, combined with a two-axis geometric notation, provides amore intuitive and logically transparent foundation for complex numbers — replacingthe historically confusing imaginary unit i with a natural coordinate system of twoperpendicular axes, each governed by its own operation pair. We verify that this rein-terpretation is mathematically equivalent to standard complex arithmetic across allmajor applications, while offering improved pedagogical clarity. The conjugate oper-ation, rotation, Euler’s formula, division, and signal processing all emerge naturallyfrom this framework without appeal to imaginary quantities.
Author: Kureshi, Sufiyan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7143361719