Complex Numbers with Mathematica: Complex Arithmetic, Methods, and Geometric Interpretations

Course Description

This is a mini crash course providing all you need to know to understand complex numbers, and study Complex Analysis. Mathematica is used to help visualize the complex plane.

Complex Numbers with Mathematica: Complex Arithmetic, Methods, and Geometric Interpretations
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Video Lectures & Study Materials

# Lecture Play Lecture
1 The imaginary unit and how to add complex numbers Play Video
2 Complex Addition and the Parallelogram Law. Use ListPlot on Mathematica to make the plot. Play Video
3 Complex Number Addition and the Parallelogram Law. Use of Mathematica to create vectors. Play Video
4 Complex Number Addition, Parallelogram Law, Triangle Inequality, and Manipulate on Mathematica Play Video
5 Modulus of a Complex Number, Triangle Inequality, Manipulate and Locator on Mathematica Play Video
6 Complex Number Subtraction in terms of Vectors, Manipulate and Locator on Mathematica Play Video
7 Introduction to Multiplying Complex Numbers and Geometrically Interpreting the Product Play Video
8 Complex Multiplication in terms of Moduli and Arguments. Use Mathematica to illustrate. Play Video
9 Confirm the Geometry of Complex Number Multiplication with Manipulate and Locator. Principal Value. Play Video
10 Complex Number Reciprocals (Multiplicative Inverses), approached Algebraically Play Video
11 Complex Multiplicative Inverses, Complex Division, and Complex Conjugates Play Video
12 Complex Conjugates, Complex Division, and Visualization on Mathematica. Play Video
13 Introduction to the Polar Form of a Complex Number and Complex Multiplication Play Video
14 Polar Form of Complex Numbers, both with "Cis" & with "e" (Euler's Formula) Play Video
15 De Moivre's Formula and Trigonometric Identities (mistake at the end...see description below) Play Video
16 De Moivre, Trig Identities, Sine and Cosine in Terms of Exponentials Play Video
17 A Real Integral done using Complex Arithmetic (Euler's Formula) Play Video
18 Check the use of Cosine as an Exponential to the Evaluation of an Integral. Play Video
19 Powers of Complex Numbers (and an intro to "Table" on Mathematica). Play Video
20 Using Mathematica to Visualize Powers of Complex Numbers Play Video
21 Dynamic Behavior of Powers of Complex Numbers, Intro to Roots and Multi-Valued Functions Play Video
22 Deriving and Graphing Complex Roots of Unity Play Video
23 Graphing Complex Roots with Mathematica Play Video
24 More on Visualizing Complex Roots with Mathematica Play Video
25 Introduction to Basic Topology of the Complex Plane (Define an Open Disk) Play Video
26 Open Sets in the Complex Plane and illustrating the definition with Mathematica Play Video


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