Complex conjugate line

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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 the line. So if the equation of DScript error: No such module "Check for unknown parameters". is D: ax + by + cz = 0Script error: No such module "Check for unknown parameters"., then the equation of its conjugate D*Script error: No such module "Check for unknown parameters". is D*: a*x + b*y + c*z = 0Script error: No such module "Check for unknown parameters"..

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

References

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