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\noindent{\Large{\textsc{Complex Variables \hfill Assignment 4.3  \\ Fall 2024 \hfill Due September 25}}}

\large

\vspace{1cm}

\begin{exercise}
Textbook exercise 1.4.5.
\end{exercise}

\begin{exercise}
Textbook exercise 1.4.10.
\end{exercise}

\begin{exercise}
Let $f(z)$ be a complex-valued function defined on a deleted neighborhood of $z_0$.  Show that if $\lim_{z \to z_0} f(z) = a$, where $a \in \C^{\times}$, then $f(z)$ is bounded away from zero on $D^{\ast}(z_0; r)$ for some $r>0$.  That is, show there are constants $M,r >0$ so that if $z \in D^{\ast}(z_0;r)$, then $|f(z)|>M$.
\end{exercise}



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