Complex numbers are very useful for streamlining a lot of different types of math, generalizing ideas, and “closing” the real numbers. In quantum theory you’ll find that on the most fundamental level the universe seems to prefer complex numbers to real numbers. Once we have the vector notion of a complex number, we can think about adding complex numbers as adding vectors. Hence, to recap, we can view complex numbers geometrically as representing points or vectors in the complex plane. If we do this, then adding complex numbers corresponds to adding together vectors, or equivalently, moving the point that the second complex number represents along the vector that the first complex number represents.