Complex numbers and matrices
Let us examine some consequences of the revelation that multiplication by i represents a rotation through a right angle about the centre of the coordinate plane. If z=x+iy, we have through expanding the brackets and reordering multiplications that i(x+iy)=-y+ix, so that the point(x，y)is taken to(-y，x)under this rotation;see Figure 15. In this way, multiplication by i can be regarded as operating on points in the plane. This operation enjoys the special property that for any two points z and w and any real number a, we have i(z+w)=iz+iw, and i(aw)=a(iw).