This is a homework question, so if I am wrong please do not explicitly give me the answer.
Question: Describe all real-valued functions which are analytic on $\mathbb{C}$.
My Answer: Given that we are describing all real-valued functions, this implies that $iv(x,y)=0$ for the equation $f(x+iy)=u(x,y)+iv(x,y)$. Thus, $u_x=v_y=0$ and $u_y=-v_x=0$.
Am I missing anything? This answer seems too easy, but I am having a hard time wrapping my head around a real-valued function being analytic with the Cauchy-Riemann equations equaling zero.