Multiplication of complex numbers

$$z_1=a_1+i{b}_1 ; a_1,b_1\in \mathrm{ℝ} , i=\sqrt{-1}$$

$$z_2=a_2+i{b}_2 ; a_2,b_2\in \mathrm{ℝ} , i=\sqrt{-1}$$

$$z_1·z_2=\left(a_1·a_2-b_1·b_2\right)+i·\left(a_1·b_2+a_2·b_1\right)$$

Difference of squares:

$$a^2-b^2=\left(a-b\right)·\left(a+b\right)$$