Consider the function where xy U = for (x, y) = (0,0), x² + y² and v= = 0 for all x and y. X 2.1 Show that all partial derivatives of u and v exist at (x, y) = (0, 0), and thus satisfy the Cauchy- Riemann equations. (5) 2.2 Show that is not continuous at (0,0), and hence f is not differentiable at (0, 0). U (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 (x, y) = x² - y² —y is harmonic and determine its harmonic conjugate. - f = u + iv,