DirectedInfinity[ ] represents an infinite numerical quantity whose direction in the complex plane is unknown.
DirectedInfinity[z] represents an infinite numerical quantity that is a positive real multiple of the complex number z.
You can think of DirectedInfinity[z] as representing a point in the complex plane reached by starting at the origin and going an infinite distance in the direction of the point z.
The following conversions are made:
Certain arithmetic operations are performed on DirectedInfinity quantities.
In OutputForm, DirectedInfinity[z] is printed in terms of Infinity, and DirectedInfinity[ ] is printed as ComplexInfinity.
See The Mathematica Book: Section 3.1.8.
See also: Indeterminate.