Rotation of Rectangle using Complex Numbers

Each vertex of the rectangle is multiplied by the complex number z producing an image of the rectangle which is the result of an enlargement and a rotation.
Rectangle ABCD is fixed. Move the complex number z around to see the effect it has on EFGH, the image of ABCD. Notice (1) the link between the modulus and the scale of the enlargement and (2) the effect that the angle of z to the real axis has on the rotation.