Carl Friedrich Gauss is said to be the inventor of visualizing complex numbers as points in the plane. Thereby the complex number a+ib is visualized by the point (a,b). Try to find out what effect adding the number 2+i has on the points. Also try to find out what effect multiplying by i has on the points of the plane. What happens if you mutltiply by -i? What happens if you multiply by 2+i? What happens if you divide by 2+i? In each case, try to express the effect geometrically. Write down your findings. Are you able to generalize your observations to adding, multiplying or dividing by general numbers? Give also a little background on Gauss, the invention of the complex number line, and the difference between this and the cartesian plane.
Erich Prisner, August 2003