(a) Let u(x, y) = 2y + ry + r and v(r, y) = r - y. (i) Determine all z E C such that f(2) = f(x + zy) = u(x, y) + iv(x, y) is differentiable in the complex sense, with z = r + zy E C, x, y E R. (ii) Find a real valued function w(r, y) such that g(z) = g(x + zy) = u(x, y) + iw(z, y) is differentiable in the complex sense for all z E C. (iii) Express g(z) in terms of z = x + zy