OurBigBook.comSite Source code

Analytic function with image in an affine real line

If

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.

 Ancestors (6)

 Incoming links (1)

Solution