# Directed infinity

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