In the complex notation there is a clever device for finding the time average of a produ...

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 – ω + δ_a) and g(r, t) = B cos (k · r − ωt + δ_b). Show that where the star denotes complex conjugation. [Note that this only works if the two waves have the same k and ω, but they need not have the same amplitude or phase.] For example,