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Terris Becker edited untitled.tex
almost 8 years ago
Commit id: 874408b8e48c401f608146b16d5554014c099dff
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\textit{Oh, an empty article!}
You can get started by \textbf{double clicking} this text block \begin{problem}[6.6]
\textit{Show that, if $f$ is holomorphic and nonzero in $G$, then $ln|f(x,y)|$ is harmonic in G.}
\end{problem}
\begin{proof}
Assume $f=u+iv$ is holomorphic and nonzero in $G$. Since $f$ is holomorphic, its real and
begin editing. You can also click the \textbf{Text} button below to add new block elements. Or you can \textbf{drag imaginary parts are harmonic and therefore infinitely differentiable by Proposition 6.4 and
drop an image} right onto this text. Happy writing! Corollary 6.9.
The first derivative of $ln|f(x,y)|$ is
\begin{align*}
(ln|f(x,y)|)_x &= [ln(\sqrt{u^{2}+v^{2}})]_x\\
&= \frac{1}{2}[ln(u^{2}+v^{2})]_x
\end{proof}
