Complex Multiplication in terms of Moduli and Arguments. Use Mathematica to illustrate.

Complex Analysis, Video #8 (Complex Arithmetic, Methods and Geometric Interpretations, Part 8). Complex Multiplication and its Geometric Interpretation. Intro to Modulus and Argument.

Details: Review complex multiplication. Review visualization using Locator on Mathematica. Verify that |z1*z2| = |z1|*|z2| using Abs on Mathematica (Abs[-14+5i] = Abs[2+3i]*Abs[-1+4i] since 13*17=221=196 + 25). The modulus of the product is the product of the modulii of the factors. The argument of a complex number. Verify that the argument of the product is the sum of the arguments of the factors by creating triangles and using trigonometry. Use the arctangent function on the triangles (via ArcTan on Mma) to confirm this.

[waynemv]

Mathematica is fine and all. But when using old technology, and using just a compass and a straightedge to find the product of two arbitrary points in the complex plane, what is the minimum number of Euclidean construction steps required?