复数与几何

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翻新时间：2023-01-19

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复数与几何

摘要

复数是中学代数课程中数的概念最后1次扩展.初学复数时,对它的存在往往会感到怀疑,认为它是虚无缥缈的数.事实上,复数的应用非常广泛,特别是在几何中的应用.本文利用复数来研究几何,主要考虑如下的问题:平面上的点集的复数表示;平面曲线的复数表示;复数在共线、共点、共圆、复数的麦比乌斯变换等几何问题上的应用,在说明这些应用的同时介绍1些数学上常用的思考方法.

关键词:复数;复数运算;平面点集;平面曲线;几何应用;复数方法;麦比乌斯变换

Complex numbers and geometry

ABSTRACT

Complex numbers is the last expansion of numbers’ concept of the algebra course in middle school. While beginning.to.learn the complex numbers,people will often feel doubtful to its existence and think it is illusory .In fact,its applications are very extensive, especially the application in geometry. This thesis makes use of complex numbers to study geometry. It mainly considers the following questions: using complex numbers to express collected points and curves on the level;geometric applications of complex numbers on collinear,concurrent,round,Mobius Mappings of Complex numbers problems,etc..Meanwhile,this thesis recommends some methods for thinking on mathematics.

Keywords:Complex numbers; Complex numbers operation; Collected points on the level; Curves on the level ; Geometric application; Complex numbers’ methods; Mobius Mappings