I am trying to find a reference for a certain concept that arises in my native language as, directly translated, "conjugated imaginary points".
The problem is this direct translation does not give me any results online because it must be named something else in English. I have seen this in the contents of a book called Descriptive Geometry written in my native language, but I have no access to this book so I am searching for other references of this concept.
I will try to provide context where this appears so maybe someone can tell me where I can read more about it. As I said it is contained in the topic of descriptive geometry and in context(of conic sections) it is used as:
Every line has two common points with a conic. If these points are real and different, we say that the line is a secant of the conic. If these two points coincide we say that the line is a tangent and if these points are conjugated imaginary then this line is a pasant(?) of a conic.
Here is also a figure for this text:
Obviously this last case of a line is one that does not even touch the conic, but I am more interested in this concept of conjugated imaginary points. I will gladly give more context if required.
When there are no intersections with the conic, the coordinates of the two imaginary intersections will be complex conjugates. That is, corresponding coordinates of the two points will be of the form $a\pm bi$. For example, the unit circle $x^2+y^2=1$ intersects the line $y=2$ at the imaginary points $(\pm\sqrt3i,2)$; the intersections of the line $x+y=2$ with this circle are $\left(1\pm\frac1{\sqrt2}i,1\mp\frac1{\sqrt2}i\right)$ .
This is a consequence of the fact that these coordinates are solutions of quadratic equations with real coefficients, complex roots of which always come in conjugate pairs.