一般地说,当动点与直角三角形、正三角形、平行四边形(含有特殊角)的顶点有关时,应用复数比较方便。仅举一例予以说明。例.边长为a的正△ABP的顶点B、A分别在x轴、y轴上滑动(A,B,P逆时针排列)。求顶点P在第一象限的轨迹。设P、A、B分别对应复数x+yi,2mi,2n,则AB中点C对应复数n+mi,那么 In general, when the moving point is related to the vertices of a right triangle, an equilateral triangle, and a parallelogram (including a special angle), it is more convenient to apply the complex number. Just give an example. For example, the vertices B and A of the positive ΔABP with side length a slide on the x-axis and y-axis, respectively (A, B, P are arranged counterclockwise). Find the trajectory of the vertex P in the first quadrant. Let P, A, and B correspond to the complex numbers x+yi, 2mi, and 2n, respectively, then the AB midpoint C corresponds to the complex number n+mi.