Complex numbers/Pairs/Definition

Complex numbers

The set ${}\mathbb {R} ^{2}$ with ${}0:=(0,0)$ and ${}1:=(1,0)$, with componentwise addition and the multiplication defined by

${}(a,b)\cdot (c,d):=(ac-bd,ad+bc)\,,$

is called the field of complex numbers. We denote it by

$\mathbb {C} .$