12. If f(z) = u+ iv is an analytic function of z = x+ iy, and u v = e" (cos y sin y), find f(z) in terms of z. Ans: f(z) = e +c. y}, where 13. Consider the function f u(x, y) = x, v(x, y) = y. Note that u, v satisfies the C-R equations in D, and u, Uy, V, Vy are also continuous in D. Prove that f is not analytic on D. Does this fact contradict the related Theorem? If not, explain why. = u + iv defined on the set D := {x + iy E C : x =