The Complex Plane 
 Exercises on Using Complex Numbers for the Geometry of the Euclidean Plane
3apr11
University of Illinois} 

\begin{document}
\maketitle


The exercises here pertain to Hvidsten's itroduction to
the  complex, pp 131 and 132. Solve the first five problems,  
Hvidsten 3.5.1 -- 3.5.5. 

\section{Additional problems.}
\begin{itemize}
\item Problem 6. Show that the dot product for vectors $(x,y)\cdot (u,v)$ is 
related to the complex product. Let $z=x+iy, w=u+iv$, show that  
\[ (x,y)\cdot(u,v)=Re(\bar{z}w} = Re(z\bar{w}) \].
\end{itemize}