Imaginary line (mathematics)
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It is a special case of an imaginary curve.
- The locus of points whose coordinates satisfy a homogeneous linear equation with complex coefficients
- is a straight line and the line is real or imaginary according as the coefficients of its equation are or are not proportional to three real numbers.
According to Hatton:
- The locus of the double points (imaginary) of the overlapping involutions in which an overlapping involution pencil (real) is cut by real transversals is a pair of imaginary straight lines.
- Hence it follows that an imaginary straight line is determined by an imaginary point, which is a double point of an involution, and a real point, the vertex of the involution pencil.