Complex Numbers

So far we have worked with real numbers and used that they are ordered and can be added and multiplied, tacitly assuming that addition and multiplication satisfy the classical computational rules, i.e., that these operations are commutative, associative, $$\ldots $$ . It turns out that for many reasons, it is necessary to consider an extension of the set $$\mathbb {R}$$ of real numbers. These more general numbers are referred to as complex numbers and the set of them is denoted by $$\mathbb {C}$$ .