Complex Analysis Video #9, (Complex Arithmetic, Part 9). Complex Multiplication and its Geometric Interpretation. Modulus and Argument. Intro to Principal Value of the Argument.
Details: Review what happens when you multiply two complex numbers. The modulus of the product is the product of the modulii of the factors. The argument of the product is the sum of the arguments of the factors. Write those two facts symbolically (using absolute value symbols for the modulii and "arg" for arguments). Experiment with the Manipulate (Locator) output to test these facts. Briefly mention the "principal value" of the argument (between -pi and pi). Show how to re-do the code using Re and Im in Mathematica). Use the Arg command in Mathematica to find the principal value of the argument.