Suppose $f:U\to \mathbb{C}$ is holomorphic. If we represent $f(x+iy)=u(x,y)+iv(x,y)$,
:?:
then $u,v$ are harmonic. i.e.

This is a corollary of 3. Theorem 2.1.1 - Cauchy-Riemann (And the theorem of Goursat). We had to assume here that $u,v$ are twice differentiable.