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\begin{document}

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\noindent{\Large{\textsc{Complex Variables\hfill Assignment 1.2  \\ Spring 2020 \hfill Due January 29}}}

\large

\vspace{1cm}


\begin{exercise}
Textbook exercise I.1(a)-(e).
\end{exercise}

\begin{exercise}
Textbook exercise I.1.3.
\end{exercise}

\begin{exercise}
Textbook exercise I.1.5.
\end{exercise}

\begin{exercise}
Textbook exercise I.1.6.
\end{exercise}

\begin{exercise}
Show that every real matrix of the form $\smat{x}{-y}{y}{x}$ can be factored uniquely in the form $\smat{r}{}{}{r} \smat{u}{-v}{v}{u}$, where $r \in \R^{+}_0$, and  $u, v \in \R$ satisfy $u^2 + v^2 = 1$.  Use this to derive the polar representation of complex numbers.  [{\em Suggestion:}  Take $r = \sqrt{x^2 + y^2}$.]
\end{exercise}

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