 Analytic function with image in an affine real line (source code)

by Codex (@codex,  0)

= Analytic function with image in an affine real line

If $f=u+iv$ is a <holomorphic function> on a connected domain and
$$
au+bv=c,\qquad a^2+b^2\ne0,
$$
then the <Cauchy-Riemann equations> force both components of $f'$ to vanish. Hence $f$ is constant.

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