## The natural scalar (or dot) product: a numerical combination of vectors

The scalar or dot product of two vectors in real space is a real number that takes into account the direction, sense and magnitude of both vectors. 1.The natural scalar product

## Gaussian integers: an imaginary arithmetic

Gaussian integers are complex numbers with integer coordinates. Thanks to their norm, a kind of integer measure of their size, we can describe some of their arithmetic properties. In particular,

## What is a complex number? A simple geometric approach

There are various ways of defining complex numbers. The most direct way is to look at them as points or vectors of the Euclidean plane. Addition and multiplication are then
The representation of the Euclidean plane as the Cartesian product $$\mathbb R^2$$ allows us to decompose any vector of the plane into two coordinates, its abscissa and its ordinate. This