(i) Which of the following is the real part of a holomorphic function. Explain your reason- ing, but you do not need to find the holomorphic function. (a) g(x, y) = e cos(x), (b) h(x, y) = x + y. (ii) Find a holomorphic function f: C C that has u(x, y) = 2x 4x - 6xy + 4y - as its real part, i.e., find a real-valued function v(x, y) such that f(z) = f(x + y) = u(x, y) + iv(x, y) for all x, y R. (iii) Express the function f from part (ii) as a function of z E C (not as a function of x and y).