# Geometrical Representations

• Walter Ledermann
Part of the Library of Mathematics book series (LIMA)

## Abstract

We have already remarked that the complex number x + iy may be thought of as an ordered pair (x, y) of real numbers. As the reader knows from co-ordinate geometry, such a pair of real numbers may be regarded as the coordinates of a point in a plane. We are thus led to the following geometrical interpretation of complex numbers: choose a plane and furnish it with Cartesian rectangular axes Ox, Oy. Let the number x+iy be represented by the point P=(x,y). In this way we can plot complex numbers as points of a plane (see Fig. 2). This plane (or more correctly such a plane) is often called the Argana plane or Argana diagram or simply the complex plane. Any algebraical proposition between complex numbers can be translated into a geometrical relation between the corresponding points of the Argand plane, and conversely, any relation between points of a plane can, in principle, be regarded as a relation between complex numbers. The reader should, however, keep the logical situation clearly in mind: we have defined complex numbers as algebraical objects obeying certain laws of composition.

## Keywords

Complex Number Geometrical Representation Polar Form Algebraical Object Logical Situation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.