Determine the value of complex function

Question

Given $f: \mathbb{C} \mapsto \mathbb{C}$ is an analytic function which expressed as $f(z) = u(x) + iv(y)$ for every complex numbers $z = x + iy$. If $f(20)= 17$ and $f(17)=20$, then the value of $f(2017) =..... $

I have some doubt here. First, does $f(20)$ here means that the domain of function is $z = 20$ (which means that $x = 20$), hence $u(20)$ will be expressed as a result? This is an analytic function, so it should be known that it satisfies and

$\dfrac{\partial u} {\partial x} = \dfrac{\partial v} {\partial y}$

and

$\dfrac{\partial u} {\partial y} = - \dfrac{\partial v} {\partial x}$

but to be honest, I can't relate this to calculate $f(2017)$. Please help.

Answer 1

Hint: If a function that depends only on $x$ is equal to a function that depends only on $y$ then both functions must be constant. Apply that to $\dfrac{\partial u} {\partial x} = \dfrac{\partial v} {\partial y}$...

Answer 2

Hint: $f$ is analytic function, so it satisfy Cauchy-Riemann Equation: $u_x = v_y$ and $u_y=-v_x$.

We know that $u$ only depends on $x$ and $v$ only depends on $y$. So, $u_x = v_y$ holds only if $u$ and $v$ is a linear functions.