View source for Directed infinity

A '''directed infinity''' is a type of infinity in the complex plane that has a defined [[Argument (complex analysis)|complex argument]] ''θ'' but an infinite absolute value&nbsp;''r''.<ref>{{MathWorld|urlname=DirectedInfinity|title=Directed Infinity}}</ref> 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:

*<math>z\infty = \sgn(z)\infty \text{ if } z\ne 0</math>
*<math>0\infty\text{ is undefined, as is }\frac{z\infty}{w\infty}</math>
*<math>a z\infty = \begin{cases} \sgn(z)\infty & \text{if }a > 0, \\ -\sgn(z)\infty & \text{if }a < 0. \end{cases} </math>
*<math>w\infty z\infty = \sgn(w z)\infty</math>

Here, sgn(''z'') = {{sfrac|''z''|{{abs|''z''}}}} is the [[Sign function#Complex signum|complex signum]] function.

== See also ==
*[[Point at infinity]]

== References ==
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