# Definition ( Complex number)

### Definition( Complex Number)

A complex number is an element (x, y) of the set $R^2$ = { $(x,&space;y)&space;:x,y&space;\in&space;R$ }

obeying the following rules of addition and multiplication

If $Z_1=(x_1,y_1),Z_2=(x_2,y_2)&space;\in&space;R^2$  then

1.     $Z_1+Z_2=(x_1+x_2,y_1+y_2)$

2.     $Z_1.Z_2=(x_1x_2-y_1y_2,x_1y_2+y_1x_2)$

as   Z= 3+4i