Complex line

In mathematics, a complex line is a one-dimensional affine subspace of a vector space over the complex numbers.[1][2] A common point of confusion is that while a complex line has dimension one over C (hence the term "line"), it has dimension two over the real numbers R, and is topologically equivalent to a real plane, not a real line.[3]

The "complex plane" commonly refers to the graphical representation of the complex line on the real plane, and is thus generally synonymous with the complex line, and not a two-dimensional space over the complex numbers.

See also

References
  1. Brass, Peter; Moser, William; Pach, János (2005), Research Problems in Discrete Geometry, Springer, New York, p. 305, ISBN 9780387299297, MR 2163782.
  2. Shabat, Boris Vladimirovich (1992), Introduction to Complex Analysis: Functions of Several Variables, Translations of mathematical monographs, vol. 110, American Mathematical Society, p. 3, ISBN 9780821819753
  3. Miller, Ezra; Reiner, Victor; Sturmfels, Bernd (2007), Geometric Combinatorics: Lectures from the Graduate Summer School held in Park City, UT, 2004, IAS/Park City Mathematics Series, vol. 13, Providence, RI: American Mathematical Society, p. 9, ISBN 978-0-8218-3736-8, MR 2383123.


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