I am confused if complex numbers really are vectors. They seem to behave as vectors in addition, but not in multiplication. So why are the complex numbers defined to be vectors although they don't follow the same principles always. Another confusing thing for me is the "complex vector", is this entity some kind of combination of a normal vector and a complex number? For example if z is a complex number and [itex]r[/itex] is an ordinary vector, what is then z*[itex]r[/itex]? Is it a complex vector?