Green's Theorem has the form: $$\oint P(x,y)dx = - \iint \frac{\partial P}{\partial x}dxdy , \oint Q(x,y)dy = \iint \frac{\partial Q}{\partial y}dxdy $$ The Cauchy-Riemann equations have the following form:(Assuming $z = P(x,y) + iQ(x,y)$) $$\frac{\partial P}{\partial x} = \frac{\partial Q}{\partial y}, \frac{\partial P}{\partial y} = - \frac{\partial Q}{\partial x}$$
Is there any connection between this two equations?