Directed infinity explained

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:

z inf ty = sgn (z) inf ty if z\ne 0 0inf ty isundefined,asis (z inf ty)/(w inf ty) a z inf ty = \begin{cases} sgn (z) inf ty & if a > 0 , \ -sgn (z) inf ty & if a < 0 . \end{cases} w inf ty z inf ty = sgn (w z) inf ty

Here, sgn(z) = is the complex signum function.

See also

• Point at infinity