] represents an infinite numerical quantity whose direction in the complex plane is unknown.
] represents an infinite numerical quantity that is a positive real multiple of the complex number z.
You can think of DirectedInfinity[
] 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[
] is printed in terms of Infinity, and DirectedInfinity[
] is printed as ComplexInfinity.
See the Mathematica book: Section 3.1.8.
See also: Indeterminate.
The FullForm of Infinity shows that it has a direction.
Here is an indeterminate form.
Infinity::indet: Indeterminate expression (-Infinity) + (Infinity) encountered.
This can be thought of as infinity along the complex axis.