You are shown part of the complex plane. The horizontal axis is the real and the vertical imaginary: a point (x,y) in the plane corresponds to a complex number x+iy. The red circle is the unit circle.

You can move the points A and B with the mouse, and the red point displays the result of an addition, multiplication, or taking the reciprocal of A, as chosen by clicking the buttons at the top.

You can also solve the second degree equation X^2 + AX + B = 0. The two roots are shown as red points. Here you can also move the roots to obtain A and B such that the equation has precisely those roots.

The java program is available here.