Multiplication of Complex Numbers as transformations
Complex number w can be multiplied by any complex number z by choosing a position for z on the Argand diagram. The number g shows the result. The angles that each complex number makes with the positive sense of the real axis are shown too.
Notice that the number w is transformed by a rotation and an enlargement. The modulus of z gives the scale of the enlargement and the angle z makes with the positive sense of the real axis gives the angle of rotation.