Definition:Extended Complex Plane
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Definition
The extended complex plane $\overline \C$ is defined as:
- $\overline \C := \C \cup \set \infty$
that is, the set of complex numbers together with the point at infinity.
Also known as
Some sources report the extended complex plane as the entire complex plane or entire $z$ plane.
The notation $\C_\infty$ can often be seen.
Also see
- Results about the extended complex plane can be found here.
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Spherical Representation of Complex Numbers. Stereographic Projection
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): extended complex plane
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): extended complex plane