CAJ | 학술논문

共轭与对称是复数系重要的运算，四元数的引入将实数域扩充到复数域，并用复数来表示平面向量。改进四元数的共轭与对称是对其进一步研究与应用的不可回避的环节之一，所以提出改进四元数共轭的定义并证明其性质，证明改进四元数是符合数系扩展原则的一种超复数。作为数学工具，其在机构学等其他领域的应用会更为广泛。
공액여대칭시복수계중요적운산，사원수적인입장실수역확충도복수역，병용복수래표시평면향량。개진사원수적공액여대칭시대기진일보연구여응용적불가회피적배절지일，소이제출개진사원수공액적정의병증명기성질，증명개진사원수시부합수계확전원칙적일충초복수。작위수학공구，기재궤구학등기타영역적응용회경위엄범。
Conj ugate and symmetry are important operations of complex numbers.The introduc-tion of quaternion has extended real numbers to complex numbers,which can be used to represent plane vectors.It is one of the inevitable links to improve the conj ugate and symmetry of quaterni-ons in further researches and applications of this field.In this paper we first defined the conj ugate of quaternions,and then we proved its nature,holding that the improved quaternion is a hyper-complex which corresponds to the numerical-system expansion principle.As a mathematical tool, it has a wider application in such fields as mechanism studies.