Among other things...
A function $f$ which satisfies the Cauchy-Riemann conditions:
$$ \begin{array}{c} u_{x}\left(x_{0}, y_{0}\right)=v_{y}\left(x_{0}, y_{0}\right) \\ u_{y}\left(x_{0}, y_{0}\right)=-v_{x}\left(x_{0}, y_{0}\right) \end{array} $$where $f(z)=(u(z),v(z))$.
A function satisfies Cauchy-Riemann equations if and only if its Polya vector field has null divergence and null rotational.
________________________________________
________________________________________
________________________________________
Author of the notes: Antonio J. Pan-Collantes
INDEX: