代数转几何：应用复数的locus

先上个匪夷所思的东西：

Fractional Linear Transformation

A fractional linear transformation is a function of the form $T(z)=\frac{(az + b)}{(cz + d)}$, where $a, b, c, d$ are complex constants and $ad-bc≠0$. These are also called Mobius transforms or bilinear transforms.

(1) Theorem: A linear fractional transformation maps lines and circles to lines and circles.

(2) Mapping of $\infty$. (the line is a considered as a circle with radius $\infty$)

(3) Composition of linear transformations are like multiplication of matrices.

(4) How to map three points on complex plane to another three points.

原理

就是每个复数可以看成复平面上的点，然后就可以固定不同的东西，比如夹角或长度或比例。

首先，可以思考一下复数的conic section。