Suppose nowthat we have two complex numbers, z and w, whose polar coordinates are(r1,θ1)and(r2,θ2)respectively. It turns out that the polar coordinates of their product zw take on a simple and pleasing form. The rule of combination can be expressed neatly in ordinary language:the modulus of the product zw is the product of the moduli of z and w, while the argument of zw is the sum of the arguments of z and w. In symbols, zw has polar coordinates(r1r2,θ1+θ2). The multiplication of the real numbers is subsumed under this more general way of looking at things:a positive real number r, for instance, has polar coordinates(r,0), and ifwe multiply by another(s,0), the result is the expected(rs,0),corresponding to the real number rs.