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Let N C C be a domain (that is, a connected open subset), and let f: N → C be holomorphic. Prove that if f (z) = iv(x, y) for every z E (namely, if the real part of the function is u = 0) then there is a constant vo E R such that f(z) = ivo in N.

Let N C C be a domain (that is, a connected open subset), and let f: N → C be holomorphic. Prove that if f (z) = iv(x, y) for every z E (namely, if the real part of the function is u = 0) then there is a constant vo E R such that f(z) = ivo in N.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let N C C be a domain (that is, a connected open subset), and let f: N → C be holomorphic. Prove that if f (z) = iv(x, y) for every z E (namely, if the real part of the function is u = 0) then there is a constant vo E R such that f(z) = ivo in N.
Transcribed Image Text:Let N C C be a domain (that is, a connected open subset), and let f: N → C be holomorphic. Prove that if f (z) = iv(x, y) for every z E (namely, if the real part of the function is u = 0) then there is a constant vo E R such that f(z) = ivo in N.
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