a) Show that , if any function is analytic it satisfies Cauchy-Riemann differential equations. b) State ratio test. Also find the region of convergence (with a scale drawing diagram) of the following series 2n=0 (n+2)(n+3) n(n+1) (z + i) 2 (4,5) c) Evaluate J(1,2) (x2 + 2xy + 1)dx + (y2 + 2x)dy along the straight line from (1,2) to (1,5) and then from (1,5) to (4,5) d) Verify Green's theorem for the integral o (2xy - x2 )dx + (x + y2)dy where C is a closed curve of the region bounded by y = x and y = x2. e) Find the residue at all the poles of the function f (z) = 3z + 2i (z - 1)2(2 - 3) (z - 2)