On a functional equation connected with a property of complex numbers

In this paper we determine the general solution of the equation [f(x) + f(y)] [f(u) + f(v)] = f(xu - yv) + f(xv + yu) for all x, y, u,v (element of) R without assuming any regularity condition on the unknown function f . This functional equation arises from a property of complex numbers and the solution of this functional equation is determined using an elementary technique.