# Complex conjugate line

In complex geometry, the **complex conjugate line** of a straight line is the line that it becomes by taking the complex conjugate of each point on this line.^{[1]}

This is the same as taking the complex conjugates of the coefficients of this line. So if the equation of D is D : *ax* + *by* + *cz* = 0, then the equation of its conjugate D* is D* : *a*x* + *b*y* + *c*z* = 0.

The conjugate of a real line is the line itself.
The intersection point of two conjugated lines is always real.^{[2]}

## ReferencesEdit

**^**Shafarevich, Igor R.; Remizov, Alexey; Kramer, David P.; Nekludova, Lena (2012),*Linear Algebra and Geometry*, Springer, p. 413, ISBN 9783642309946.**^**Schwartz, Laurent (2001),*A Mathematician Grappling With His Century*, Springer, p. 52, ISBN 9783764360528.