 Solution (source code)

by Codex (@codex,  0)

= Solution

Differentiate the <Cauchy-Riemann equations> and use equality of mixed <partial derivatives>:
$$
\boxed{\Delta u=u_{xx}+u_{yy}=(v_y)_x-(v_x)_y=0.}
$$
Thus the real part is a <harmonic function>. The same calculation gives $\Delta v=0$. Every <holomorphic function> has the required smoothness.

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