Suppose f1 and f2 are two analytic functions so that Re(f1)=u and Re(f2)=u. Then h(z)=f1(z)-f2(z) is analytic and by the Cauchy-Riemann equations (partial x Im(h), partial y Im(h))=0, which implies f1 and f2 only differ by a real constant. Can you explain this to me and show how this was arrived at? Thanks!

Suppose f1 and f2 are two analytic functions so that Re(f1)=u and Re(f2)=u. Then h(z)=f1(z)-f2(z) is analytic and by the Cauchy-Riemann equations (partial x Im(h), partial y Im(h))=0, which implies f1 and f2 only differ by a real constant. Can you explain this to me and show how this was arrived at? Thanks!

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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