Why not a complete duplicate ( though a partial one) : This question deals both with multiplication of complex numbers,and with addition; hence , with the general idea of performing a binary operation on ordered pairs of reals. So, it is a bit more general as another post ( linked below) , and , as such, may be useful for complex numbers beginners, like me.
Complex numbers are defined as elements of $\mathbb R^2$, that is, ordered pairs of real numbers.
So, in a way, binary operations on complex numbers - such as addition or multiplication - are similar to adding or multiplicating points.
Can these operations be represented as movements in the real plane, in the same way as addition of integers is represented, at the basic level, as a movement on a line , or rather, on a series of aligned dots.
Maybe adding two complex numbers is analogous to moving from one point to another?
But I can't imagin to what movement could correspond multiplying two complex numbers.
Note : in comments, a link to a very helpful video by 3Blue1Brown.