Introduction to Multiplying Complex Numbers and Geometrically Interpreting the Product

Complex Analysis Video #7 (Complex Arithmetic, Methods and Geometric Interpretations, Part 7). Complex Multiplication and Intro to its Geometric Interpretation.

Details: Review complex subtraction from previous videos, including details about the diagram. Complex multiplication (2 + 3i)*(-1 + 4i). Make a guess about how to it by using FOIL on binomials...with the caveat that i^2 = -1. This is indeed how to do it. General rule for complex multiplication given. Use of double square bracket notation on Mathematica to pick off the first and second coordinates of a point (representing the real and imaginary parts, respectively, of complex numbers). Plot the product. Describe the geometric interpretation verbally.