Page "Cauchy–Riemann equations" Paragraph 47

Owing respectively to Green's theorem and the divergence theorem, such a field is necessarily conserved and free from sources or sinks, having net flux equal to zero through any open domain.

( These two observations combine as real and imaginary parts in Cauchy's integral theorem.

) In fluid dynamics, such a vector field is a potential flow.

In magnetostatics, such vector fields model static magnetic fields on a region of the plane containing no current.

In electrostatics, they model static electric fields in a region of the plane containing no electric charge.