Riemann sphere
Extended complex numbers

The extended complex numbers consist of the complex numbers C {\displaystyle \mathbf {C} } together with ∞ {\displaystyle \infty }. The set of extended complex numbers may be written as C ∪ { ∞ } {\displaystyle \mathbf {C} \cup \{\infty \}}, and is often denoted by adding some decoration to the letter C {\displaystyle \mathbf {C} }, such as

The notation C ∗ {\displaystyle \mathbf {C} ^{*}} has also seen use, but as this notation is also used for the punctured plane C ∖ { 0 } {\displaystyle \mathbf {C} \setminus \{0\}}, it can lead to ambiguity.

Geometrically, the set of extended complex numbers is referred to as the Riemann sphere (or extended complex plane).
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