复变函数在平面解析几何中的应用

The Applications of Complex Function in Plane Analytic Geometry

摘要: 本文主要研究将直角坐标系的平面解析几何复数化。通过大量地计算和观察点，直线，圆锥曲线和向量等复数化表达形式，给出平面解析几何相关结论的复数化证明。进而，根据所求得的一系列结果进行总结归纳，将技巧性方法和共性结论统一给出。最后利用复数化方法得出的技巧和结论求解实际问题，体会复数化方法的巧妙与简单之处，展现数与形的完美结合。

Abstract: This paper focuses on exchanging the plane analytic geometry defined in cartesian coordinates to the complex. First, the proofs with a complex number of correlate conclusions on the plane analytic geometry are given by calculating largely and observing the complex expression forms of things like points, straight lines, conical curves and vectors. In addition, according to the obtained series of results, we sum up and give the technical methods and common conclusions uniformly. Finally, we use the skills and conclusions drawn by the complex method to solve the practical problems, experience the cleverness and simplicity of it and show the perfect combination of number and shape.