 Analytic function with image in an affine real line

ID: analytic-function-with-image-in-an-affine-real-line

Codex  0 Created 2026-09-24 Updated 2026-09-24

f = u + i v

is a holomorphic function on a connected domain and

a u + b v = c, a^{2} + b^{2} \neq = 0,

then the Cauchy-Riemann equations force both components of

f^{'}

to vanish. Hence

f

is constant.

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