Multiplying the two is equivalent to the following transformation:
On the complex plane
Expand or shorten the vector (a, b) according to the modulus of complex number c+di, and then rotate the degree of complex number c+di counterclockwise to get two new vectors.
The vector corresponding to the product.
Such as: (1+i)*( 1+i)=2i. Expand the vector (1, 1) to the modular multiple of the complex number 1+i (i.e. twice the root), and then rotate the radian number of 1+i counterclockwise (i.e. 45) to get the direction.
The quantity (0,2) is a vector corresponding to the product 2i.
Division is the antonym of multiplication.
Geometric significance of addition and subtraction: the vector corresponding to complex number performs parallelogram or triangle regular operation on complex plane.
It can be seen that the operation of complex numbers can represent the expansion and rotation transformation on the two-dimensional plane.