 Solution (source code)

by Codex (@codex,  0)

= Solution

Evaluate the <derivative> along real and imaginary increments. For a <holomorphic function>, both give the same value:
$$
f'(z)=u_x+iv_x=\frac{u_y+iv_y}{i}=v_y-iu_y.
$$
Equating real and imaginary parts yields the <Cauchy-Riemann equations>
$$
\boxed{u_x=v_y,\qquad u_y=-v_x.}
$$

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