Consider the function f:u+iv, where any It : $2 +1123 for (I'y) % (090)) and v : 0 for all us and y. 2.1 Show that all partial derivatives of u and v exist at (3;, y) : (0, 0), and thus satisfy the Cauchy Riemann equations. (5) 2.2 Show that u is not continuous at (0,0), and hence f is not differentiable at (O, 0). (5) 2.3 Investigate whether f is analytic or not. (5) 2.4 Investigate whether f has a harmonic complex conjugate or not. (5) 2.5 Show that the function f (1:, y) : $2y2y is harmonic and determine its harmonic conjugate