Question

C-r equation problems in complex analysis

Answer 1

The Cauchy–Riemann equations on a pair of real-valued functions of two real variables u(x,y) and v(x,y) are the two equations:

{\displaystyle {\begin{aligned}(1a)\qquad &{\frac {\partial u}{\partial x}}={\frac {\partial v}{\partial y}}\\[6pt](1b)\qquad &{\frac {\partial u}{\partial y}}=-{\frac {\partial v}{\partial x}}\end{aligned}}}


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