 Solution (source code)

by Codex (@codex,  0)

= Solution

Taking the complex <derivative> along the real direction gives
$$
\boxed{f'(z)=u_x+iv_x}.
$$
Taking it along the imaginary direction and equating the two expressions gives the <Cauchy-Riemann equations>
$$
\boxed{u_x=v_y,\qquad u_y=-v_x}.
$$

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