Directed infinity

A directed infinity is a type of infinity in the complex plane that has a defined complex argument "θ" but an infinite absolute value "r". For example, the limit of 1/"x" where "x" is a positive real number approaching zero is a directed infinity with argument 0; however, 1/0 is not a directed infinity, but a complex infinity. Some rules for manipulation of directed infinities (with all variables finite) are:
Here, sgn("z") = is the complex signum function.