In geometry, in the context of a real geometric space extended to (or embedded in) a complex projective space, an imaginary point is a point not contained in the embedded space.
Contents
Definition
In terms of homogeneous coordinates, a point of the complex projective plane with coordinates (a,b,c) in the complex projective space for which there exists no complex number z such that za, zb, and zc are all real.
This definition generalizes to complex projective spaces. The point with coordinates
is imaginary if there exists no complex number z such that
are all real coordinates.
Properties
Every imaginary point belongs to exactly one real line, the line through the point and its complex conjugate.
References
Imaginary point Wikipedia(Text) CC BY-SA