let $G$ be a region, and $f$ and $g$ be holomorphic function on $G$. if $\bar{f}\cdot g$ is holomorphic, show that either $f$ is a constant or $g(z)=0$ for all $z$ in $G$.
Show either $f$ is constant or $g(z)=0$ for all $z$ in the region
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complex-analysis
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3What does f(bar)*g mean? – 2012-05-19
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0Have you tried using the Cauchy-Riemann equations? The result should fall out of writing f and g in terms of their real and imaginary parts and fiddling around a bit. @Andres: bar denotes the complex conjugate. You can't tell if he means the conjugate of f or evaluating f on the conjugate of z. – 2012-05-19
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0"You can't tell if he means the conjugate of f or evaluating f on the conjugate of z." And therefore the question. – 2012-05-19
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0And what does this have to do with analytic geometry? – 2012-05-19
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0thx for the reply! f(bar) is f conjugate, and it says f(bar) time g is holomorphic. and the hint is that we suppose to use the identity theorem. – 2012-05-19
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0how do i use identity theorem to show that? well, i know if f and f¯ are holomorphic then f is constant, then im done with the first part. but what about the second part. g=0? – 2012-05-19