Complex Numbers and Functions

Abstract

One of the advantages of dealing with the real numbers instead of the rational numbers is that certain equations which do not have any solutions in the rational numbers have a solution in real numbers. For instance, x ² = 2 is such an equation. However, we also know some equations having no solution in real numbers, for instance x ² = - 1, or x ² = — 2. We define a new kind of number where such equations have solutions. The new kind of numbers will be called complex numbers.