A complex number z can be written z=x+iy. In the Argand plane the real part (x) is represented by a value on the horizontal x axis and the imaginary part (y) by a value on the vertical axis. So z is the point (x,y). A second point (x1,y1) represents another complex number z1=x1+iy1. Addition is performed by separately adding the relevant coordinates and the point (x+x1,y+y1) represents z+z1. Subtraction is similarly represented, for example, the point (x-x1,y-y1), representing z-z1.
The complex numbers can be regarded as vectors and diagrammatically represented by a line from the origin in the Argand plane to the point (x,y) where z=x+iy. The length of the line, |z| is sqrt(x^2+y^2). The addition and subtraction of complex numbers can be treated similar to addition and subtraction of vectors.