REIMAGINING COMPLEX NUMBERS Page No: 5201-5219

Christopher C. O’Neill

Keywords: Quaternions, octonions, sedenions, complex plane, mathematical operators, quadratic equation, logic Gate algebra.

Abstract: This work starts by examining the square root problem, i.e. (–1)1/2. By looking for practical solutions to this problem, it arrives at a new mathematical space, where imaginary numbers can be reinterpreted free from their algebraic context and therefore from an entirely different perspective. This new mathematical space is based on XNOR logic gates and deals strictly with operators. Further permutations of this method lead to a total of 16-dimensional gate operator spaces, which may have some application to Quantum Mechanics.



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