This meeting, we branched into a new way of thinking about the complex number system geometrically. In complex analysis, one learns that the complex numbers are graphed on a type of three-dimensional graph called a Riemann sphere (named after Bernhard Riemann). Fig. 3-1 below depicts the type of graph visually.
[Fig 3-1 - The Riemann sphere, with labeled terms].
The illustration above attempts to show how a complex number is graphed onto the Riemann sphere - the complex number (e.g. 3 + 4i) is graphed with a coordinate of the form (x, y, z).