Imaginary point

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

${\displaystyle (a_{1},a_{2},\ldots ,a_{n})}$

is imaginary if there exists no complex number z such that

${\displaystyle (za_{1},za_{2},\ldots ,za_{n})}$

are all real coordinates.[1]

Every imaginary point belongs to exactly one real line, the line through the point and its complex conjugate.[1]

• Real point