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 complex dimension one over C (hence the term "line"), it has ordinary 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, not the complex coordinate plane.
See also
editReferences
edit- ^ Brass, Peter; Moser, William; Pach, János (2005), Research Problems in Discrete Geometry, Springer, New York, p. 305, ISBN 9780387299297, MR 2163782.
- ^ 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
- ^ 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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