Using The Complex Square Root Formula And Pythagorean Triples To Take Square Roots Of Quaternions, Tessarines, Split Complex Numbers, and Modular Tessarines

摘要

#$%^&*AU2018100498A420180524.pdf#####Using The Complex Square Root Formula And Pythagorean Triples To Take Square Roots Of Quaternions, Tessarines, Split Complex Numbers, and Modular Tessarines Paul C. Bingham Cheffers 14 April 2018 1 Abstract Abstract Australian Innovation Patents 1. #2017101121: The Complex Square Root Formula In Modular Arithmetic And Pythagorean Triples 2. #2017101124: The Complex Square Root Formula In Modular Arithmetic And Pythagorean Triples, Part B show a way to take a modular square root of a modular complex number mod p*q (for 1 mod 4 semiprimes) when one of the square roots of -1 is known. In this method all intermediate results are natural squares so that no modular square root needs to be taken. This patent extends the Pythagorean Triple method of taking square roots, through the Complex Square Root formula, to other constructs having imaginary numbers, including Quaternions, Tessarines, Modular Tessarines, and Split Complex Numbers. Two methods of taking square roots of Quaternions are given, including one where the Quaternion is described by a+b*UNITVECTOR. 1