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