Complex Analysis - Analytic Functions

Let f(z) be an analytic function, where z = x + iy. If the real part of f(z) is cosh x cos y, and the imaginary part of f(z) is zero for y = 0, then f(z) is

If $f(z) = (x^2 + ay^2) + ibxy$ is a complex analytic function of $z = x + iy$, where $i = \sqrt{-1}$, then