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\begin{document}


\begin{enumerate}
\item  \label{one}
	Convert the following complex numbers to trig form ($re^{i\theta}$).
	You should do this by hand first and then see if your calculator can help you.
	Also, make sure you double check that the angle you find is in the right quadrant.
	\begin{enumerate}
	\item  $2+2i$
	\item  $-1+\sqrt{63}i$
	\item  $3-3\sqrt{3}i$
	\item  $-3\sqrt{5}-2i$
	\item  $-3+7i$
	\end{enumerate}

\item  Convert the following complex numbers to standard form ($a+bi$).
	Double check with your calculator.
	\begin{enumerate}
	\item  $5e^{i\pi}$
	\item  $\sqrt{5}e^{(4.2487)i}$
	\end{enumerate}

\item  Multiply and divide the following complex numbers.  
	Do it two ways: the ``normal'' way and then by first converting to trig form (see problem~\ref{one}).
	Check your answers with your calculator.
	\begin{enumerate}
	\item  $(-1+\sqrt{63}i)(2+2i)$
	\item  $(-3\sqrt{5}-2i)(-3+7i)$
	\item  \[ \frac{-1+\sqrt{63}i}{2+2i} \]
	\item  \[ \frac{-3\sqrt{5}-2i}{-3+7i} \]
	\end{enumerate}

\item  Find the following powers.  Convert to trig form first (see problem~\ref{one}).
	Put your answer in both trig form and standard form.
	Remember to check your answer with your calculator.
	\begin{enumerate}
	\item  $(2+2i)^5$
	\item  $(-1+\sqrt{63}i)^3$
	\item  $(-3+7i)^{-3}$ (What does a negative exponent mean?)
	\end{enumerate}

\item  Find the following roots.  Remember to find ALL the roots.
	\begin{enumerate}
	\item  Find all fifth roots of $1$ (there should be five different ones).
	\item  Find all cube roots of $2+2i$
	\item  Find all square roots of $-3\sqrt{5}-2i$.
	\item  Find all fouth roots of $-3+7i$
	\end{enumerate}
\end{enumerate}










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