Question

Describe Cauchy Riemann Equations

Answer 1

The Cauchy Riemann equations consist of a system of two partial differential equations which together form a necessary and sufficient condition for a complex function to be complexly differentiable that is holomorphic with a certain continuity and differentiability criteria.

The Cauchy–Riemann equations on a pair of real-valued functions of two real variables

$u(x,y)andv(x,y)$ are the two equations.

It is given by $\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}$ or

$\frac{\partial u}{\partial y}=\frac{\partial v}{\partial x}$

$uandv$ are taken to be the real and imaginary parts respectively.