For each function f listed in exercises 8 to 11, find an analytic function f with f' = f. 8. f(z) = z - 2 9. f(z) = z^4 + 1/z^2 10. f(z) = sin z cos z 11. f(z) = cos h (2z) 12. let f and g be analytic on a domain. show that (a) f + g is analytic on d and (f + g)' = f' + g': (b) fg is analytic on d and (fg)' = f' g + fg': (c) f/g is analytic at all points z_0, where g(z_0) notequalto 0 and (f/g)' = f' g - fg'/g^2. 13. show that if f is analytic on a domain d and g is analytic on a domain ohm containing the range of f, then g(f(z)) is analytic on d, and the chain rule holds: (g(f(' = g' (f(z)) f'(z). 14. let p(z) = a(z - z_1) .. (z - z_n), where a and z_1, z_n are complex numbers and a notequalto 0. show that p'(z)/p(z) = sigma^n_j=1 1/z - z_j, z notequalto z_1, z_n.