In the complex notation there is a clever device for finding the time average of a product. Suppose f(r, t) = Acos (k ?? r ?? wt + δa) and g(r, t) = B cos (k ?? r ?? wt + δb). Show that (fg) = (1/2) Re (fg*), where the star denotes complex conjugation. [Note that this only works if the two waves have the same k and co, but they need not have the same amplitude or phase.] For example

(u) = = Re(c * + -_-B B*) and (S) 140 = 1 2440 -Re(E B*). X