Imaginary point
In geometry, in the context of a real geometric space extended to a complex projective space, an imaginary point is a point not contained in the embedded space.Definition
In terms of homogeneous coordinates, a point of the complex projective plane with coordinates 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.
