Imaginary point
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.
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.[1]
Properties
Every imaginary point belongs to exactly one real line, the line through the point and its complex conjugate.[1]
gollark: Alas, such is life.
gollark: Yay, one of my nebulae grew up!
gollark: You may not want them, but would want a different thing; hence, trading.
gollark: CB rareishes which some don't like, misbreeds, etc.
gollark: There are dragons which I gather a bit which I don't want much *but* which have high trade value.
See also
References
- Pottmann, Helmut; Wallner, Johannes (2009), Computational Line Geometry, Mathematics and visualization, Springer, pp. 54–55, ISBN 9783642040184.
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