complex variable

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

An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x, y)+iv(x, y)$. Then, $u(x, y)$ and $v(x, y)$ must satisfy