Question

已知点A坐标x0,y0,求点A顺时针旋转m弧度后的点A'坐标

Answer 1

A点旋转,绕哪个点呀?

如果是绕原点顺时针旋转的话,可用复数乘法的几何意义去求.

复平面上点A对应的复数为x0+iy0,顺时针旋转m弧度可交此复数乘以cos(-m)+isin(-m).

得到复数(x0+iy0)[cos(-m)+isin(-m)]=x0cosm+y0sinm+i(y0cosm-x0sinm)

旋转后对应点的坐标为（x0cosm+y0sinm,y0cosm-x0sinm).