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

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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.

\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
$(x,y)\cdot(u,v)=Re(\bar{z}w} = Re(z\bar{w})$.