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:

*$z\infty = \sgn(z)\infty \text z\ne 0$
*$0\infty\text\frac$
*$a z\infty = \begin \sgn(z)\infty & \texta > 0, \\ -\sgn(z)\infty & \texta < 0. \end$
*$w\infty z\infty = \sgn(w z)\infty$

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

See also

*Point at infinity

References

Infinity

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