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}