information:highlighting, information:extraction
Addition and subtraction

Two complex numbers a = x + y i {\displaystyle a=x+yi} and b = u + v i {\displaystyle b=u+vi} are added by separately adding their real and imaginary parts. That is to say:

a + b = (x + y i) + (u + v i) = (x + u) + (y + v) i. {\displaystyle a+b=(x+yi)+(u+vi)=(x+u)+(y+v)i.} Similarly, subtraction can be performed as a − b = (x + y i) − (u + v i) = (x − u) + (y − v) i. {\displaystyle a-b=(x+yi)-(u+vi)=(x-u)+(y-v)i.}

The addition can be geometrically visualized as follows: the sum of two complex numbers a and b, interpreted as points in the complex plane, is the point obtained by building a parallelogram from the three vertices O, and the points of the arrows labeled a and b (provided that they are not on a line). Equivalently, calling these points A, B, respectively and the fourth point of the parallelogram X the triangles OAB and XBA are congruent.