If z1 and z2 are complex numbers, they can be represented graphically in an x-y plane if z1=x1+iy1 and z2=x2+iy2. These together with the origin (0,0) look like two sides of a parallelogram, with lines extending from the origin to the points (x1,y1) (point p) and (x2,y2) (point q). z1+z2 (point r) correspond to the point (x1+x2,y1+y2). p and q can each be joined to r forming a quadrilateral. The line op from the origin to (x1,y1) has length sqrt(x1^2+x2^2). The line oq has length sqrt(x2^2+y2^2). The line qr has length sqrt((x1+x2-x2)^2+(y1+y2-y2)^2)=sqrt(x1^2+x2^2), same as op. Similarly pr has the same length as oq. The side op makes an angle=tan^-1(y1/x1) with the x-axis and the side qr makes an angle tan^-1((y1+y2-y2)/(x1+x2-x2) with the horizontal axis. These angles are therefore equal so side qr is parallel to op. Similarly we can show that oq and pr have the same inclination. So we have two pairs of parallel sides, therefore oprq is a parallelogram.