It is known that given a harmonic function $u$ of class $C ^ {2}$ defined in a simply connected subset of $\mathbb{C}$ , we can find a function $v$ also harmonic, such that $f = u + iv$, is a holomorphic function.
What does this definition mean geometrically?
Would there be applications of this in physics?
Comments or references, are very welcome!!
Contours of constant $u(x,y)$ and $v(x,y)$ will be crossing orthogonally. For example, the harmonic conjugate of $x$ is $y$.