The set R 2 {\displaystyle {}\mathbb {R} ^{2}} with 0 := ( 0 , 0 ) {\displaystyle {}0:=(0,0)} and 1 := ( 1 , 0 ) {\displaystyle {}1:=(1,0)} , with componentwise addition and the multiplication defined by
is called the field of complex numbers. We denote it by