In mathematics, complex geometry is the application of complex numbers to plane geometry. Rather than represent a point in the plane as a pair of Cartesian coordinate system, it can be represented as a single complex number, which can be written at will in either rectangular or polar form. Complex analytical geometry deals with solving geometrical problems, especially those involving angles, by means of complex number. Using Euler's formula, : it is possible to represent any rotation as a complex number. Complex numbers can therefore be used to advantage to solve problems in elementary geometry. This method is sometimes used in the advanced high-school mathematics, since it allows schoolchildren to write down angle relations in terms of simple formulas. ==See also== *Conformal map *Complex manifold *Riemann surface Geometry
I am tempted to redirect this to complex plane. The fundamental theorem has nothing to do with geometry, and Gauss' ruler-and-compass constructions were not proved using complex numbers to my knowledge. If those to items are removed from the article, there's really nothing much left. The geometry of complex numbers is already explained in complex number. User:AxelBoldt 19:47 Feb 22, 2003 (UTC) : Well, it sounds like a good idea... but we'd need an actual article at Complex plane instead of a redirect to complex number! -- User:Tarquin 21:47 Feb 22, 2003 (UTC) If this is supposed to be about the geometry of the complex plane, then perhaps prominence should be given to the fact that the only holomorphic bijections of complex ''projective'' 1-space to itself are linear fractional transformations, which preserve circles (a straight line being regarded as a circle that passes through the point at infinity). User:Michael Hardy 21:50 Feb 22, 2003 (UTC)
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Complex geometry
In mathematics, complex geometry is the application of complex numbers to plane geometry. Rather than represent a point in the plane as a pair of Cartesian coordinate system, it can be represented as a single complex number, which can be written at will in either rectangular or polar form. Complex analytical geometry deals with solving geometrical problems, especially those involving angles, by means of complex number. Using Euler's formula, : it is possible to represent any rotation as a complex number. Complex numbers can therefore be used to advantage to solve problems in elementary geometry. This method is sometimes used in the advanced high-school mathematics, since it allows schoolchildren to write down angle relations in terms of simple formulas. ==See also== *Conformal map *Complex manifold *Riemann surface Geometry
Complex geometry
I am tempted to redirect this to complex plane. The fundamental theorem has nothing to do with geometry, and Gauss' ruler-and-compass constructions were not proved using complex numbers to my knowledge. If those to items are removed from the article, there's really nothing much left. The geometry of complex numbers is already explained in complex number. User:AxelBoldt 19:47 Feb 22, 2003 (UTC) : Well, it sounds like a good idea... but we'd need an actual article at Complex plane instead of a redirect to complex number! -- User:Tarquin 21:47 Feb 22, 2003 (UTC) If this is supposed to be about the geometry of the complex plane, then perhaps prominence should be given to the fact that the only holomorphic bijections of complex ''projective'' 1-space to itself are linear fractional transformations, which preserve circles (a straight line being regarded as a circle that passes through the point at infinity). User:Michael Hardy 21:50 Feb 22, 2003 (UTC)
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