Directed infinity

A directed infinity is a type of infinity in the complex plane that has a defined angle θ but an infinite absolute value r.^[1] For example, the limit of 1/x where x is a positive number approaching zero is a directed infinity with angle 0; however, 1/0 is not a directed infinity, but a complex infinity. Some rules for manipulation of directed infinities are:

$z\infty ={\frac {z}{\left|z\right|}}\infty .$
$0\infty =1{\text{, }}{\frac {z}{w}}={\frac {z\infty }{w\infty }}$
$az\infty ={\begin{cases}z\infty &{\text{if }}a>0,\\-z\infty &{\text{if }}a<0.\end{cases}}$
$w\infty z\infty =(wz)\infty$

See also

Point at infinity

References

↑ Weisstein, Eric W. "Directed Infinity". MathWorld.

This article is issued from Wikipedia - version of the 2/18/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.