complex geometry In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and ...

, the complex conjugate line of a

straight line In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word ''line'' may also refer to a line segment ...

is the line that it becomes by taking the

complex conjugate In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a and b are real, then) the complex conjugate of a + bi is equal to a - ...

of each point on this line. This is the same as taking the complex conjugates of the

coefficients In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves ...

of the line. So if the equation of is , then the equation of its conjugate is . The conjugate of a

real line In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a poin ...

is the line itself. The

intersection point In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their ...

of two conjugated lines is always real..

References

{{DEFAULTSORT:Conjugated Line Complex numbers