Suvarna Garge (Editor)

Directed infinity

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A directed infinity is a type of infinity in the complex plane that has a defined angle θ but an infinite absolute value r. 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 ∞ = z | z | ∞ .
  • 0 ∞ = 1 ,  z w = z ∞ w ∞
  • a z ∞ = { z ∞ if  a > 0 , − z ∞ if  a < 0.
  • w ∞ z ∞ = ( w z ) ∞
  • References

    Directed infinity Wikipedia


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