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\begin{document}

\begin{center}
{\Large TEST 4

Math 106 - 3}
\end{center}
\vspace{.1in}
You have 50 minutes to complete the test.
If it says, ``no calculator'', make sure I can follow your work without 
a calculator.
Show all relevant work (or else no credit).  
Make your work legible, if I can't read it, I can't grade it.  
Every problem is worth 10 points.
(There are only 50 points possible).

LAST TEST: TUESDAY, JUNE 2

\vspace{.1in}



Name \rule{5in}{.2pt}

\vspace{.2in}


\begin{enumerate}

\item  (20 points) Solve the triangle (Find all sides and angles)

\tri{10}{5}{7}{}{}{}
%\vspace{2in}
\newpage

\item  (10 points) Without a calculator,
write the complex number $z=\sqrt{3}-i$ in trigonometric form $z=re^{i\theta}$.

\vspace{3in}

\item (5 points extra credit)  Without a calculator, find $(\sqrt{3}-i)^9$.
Write your answer in standard form ($a+bi$).  Hint: Use previous problem.
%\vspace{3in}
\newpage

\item  (10 points) 
Find an equation of a parabola with directrix $x=5$ and focus $(1,3)$.
\vspace{3.5in}

\item (10 points)
Find the vertex, focus and directrix of the parabola:
\[
x^2-4x+4y=0
\]





\end{enumerate}


\end{document}