1) Give the points at which the given function is not analytic; z z + 3i a) f(z) = b) f(z) = c) f(z) = d) f(z) = b) lim z 1 2i z - 2z +5iz z+z z + 4 2) Show that f(2)=z and f(2)= z.zare both nowhere differentiable 3) Show that the given limit does not exist a) lim z+5-7i z +62 +25 b) f(z) = x+y=1 z - 1 4) Using the analyticity criterion show that the given functions are analytic, stating the appropriate domains and find f'(z) x-1 a) f(z)=- (x-1) + y x + xy + x x + y - y (x - 1) + y - xy + y y x + y c) f(z) = e(cos y + i sin y) d) f(z)=z e) f(z) = sin z 5) Show that the Cauchy - Riemann equations in polar coordinates are: du dr du 20 11 = ete le r de dr