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.^{[1]} 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) = z/|z| is the complex signum function.
See also
References
- ^ Weisstein, Eric W. "Directed Infinity". MathWorld.
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