Complex numbers and (2D) vectors/matrices are different representations of multi-dimensional number systems. For each operation over one, you can find an analogous operation in the other.
You can even find attempts to mix the two representations, like i+j+k vector syntax. But matrices generalize better to higher dimensions and are easier to parse.
You can even find attempts to mix the two representations, like i+j+k vector syntax. But matrices generalize better to higher dimensions and are easier to parse.