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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 $G$.

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    What does f(bar)*g mean?2012-05-19
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    Have 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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    "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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    And what does this have to do with analytic geometry?2012-05-19
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    thx 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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    how 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

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