复向量的一些几何应用摘要 回顾复向量的相关概念，通过向量与复数的运算律和运算法则的比较，归纳了复向量的性质 ，总结了平面几何和解析几何中几种常见曲线的复数表示。通过具体例题给出复向量的六类几何应用 ：判断复数在复平面象限的应用；证明不等式中的应用；求最值中的应用；求轨迹中的应用；求特定复数中的应用；平面几何中的应用。总结出运用复向量解题的大致步骤为：将已知条件转化为复向量，通过图像或复向量的性质进行解题。综合来看，复向量的几何应用实际就是数形结合思想的体现。关键词 复向量 几何应用 数形结合Some geometric applications of complex vectorsAbstract In this paper, the concept of complex vector is reviewed, and the properties of complex vector are summarized by comparing the operation law and operation law of vector and complex number, and the complex representation of several common curves in plane geometry and analytic geometry is summarized. Six kinds of geometric applications of complex vector are given through specific examples: the application of judging complex number in complex plane quadrant; the application in proving inequality; the application in finding maximum value; the application in finding locus; the application in finding specific complex number; the application in plane geometry. The steps of solving problems with complex vectors are summarized as follows: transforming known conditions into complex vectors, and solving problems through the properties of images or complex vectors. Generally speaking, the application of complex vector geometry is the embodiment of the idea of combination of number and shape.Key words Complex vector geometric application combination of number and shape目 录1.复向量的基本概念及性质..........................................................11.1 复向量的概念...................................................................11.2 向量与复数运算律和运算法则的比较....
