(Complex exponential, de Moivre's formula.) (a) Let f(t) = cost + isint. (i) Show that f(t) f(-t) = 1 for all t. (So f(-t) = 1/f(t). ) (ii) Show that f'(t) = if(t) for all t. (b) For n 2 0 let g(t) = f"(t)f(-nt). Using the preceding properties, compute (and completely simplify!) (i) g(0), (ii) g'(t)