Abel's theorem in problems and solutions - School of Mathematics

58 Chapter 2
2.4 Geometrical descriptions of the
complex numbers
Consider on the plane a system of orthogonal coordinates and let
us associate to every complex number the point of the plane with
coordinates We obtain a bijective correspondence between all complex
numbers and all points of the plane. This is the first geometrical
representation of the complex numbers.
217. Which complex numbers correspond to the points shown in
Figure 13?
FIGURE 13 FIGURE 14
218. Let the complex numbers be represented by the points of the
plane. What is the geometrical meaning of the mapping if for every
complex number a) b) c) is the
conjugate of
Let and be two points of the plane (Figure 14).
The segment AB directed from A to B is called the vector The
coordinates of the vector are by definition calculated in the following
way:
Two vectors are considered equal if they are parallel and have the
same direction and the same length.