复数_旋转

不管四元数和3D的旋转，我先要弄清楚复数和2D旋转：

cos(b) * r = x  =>  cos(b) = x / r        (1)

sin(b) * r = y   =>  sin(b) = y / r         (2)

 

cos(a + b) * r = x'    =>    cos(a)cos(b) - sin(a)sin(b) = x'        (3)

sin(a + b) * r = y'    =>    sin(a)cos(b) + cos(a)sin(b) = y'        (4)

 

把(1),(2)代入(3),(4)中：

x' = cos(a)x - sin(a)y

y' = sin(a)x + cos(a)y

 

这样(x + yi)(cos(a) + sin(a)i) = (cos(a)x - sin(a)y) + (sin(a)x + cos(a)y)i