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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.
Original languageEnglish
Pages (from-to) 5201-5219
Number of pages19
JournalCanadian Journal of Pure & Applied Sciences
Issue number2
Early online date2 Jun 2021
Publication statusPublished (in print/issue) - 2 Jun 2021


  • Quaternions
  • octonions
  • sedenions
  • complex plane
  • mathematical operators
  • quadratic equation
  • logic Gate alegrab


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