Complex Numbers pp 14-32 | Cite as

# Geometrical Representations

## 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## Preview

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