Complex Numbers

Complex Numbers

In this unit, you will explore how complex numbers can be used to generate fractals. "The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel."

-Benoit Mandelbrot (Polish/French mathematician; 1924 - 2010)

Click on a link to jump ahead to the following sections:

Lessons

Introduction to Fractals
- 5.01 Investigation - Introduction to Fractals
- 5.02 Sierpinski - More fractal investigations
- 5.02 Koch and Levy - More fractal investigations
- 5.03 Cantor - Even more fractal investigations

Lesson 1: Introduction to Complex Numbers
- 5.1 Investigation - Simple Arithmetic
- 5.1 Practice - Simple Arithmetic - Practice

Lesson 2: Complex Graphing
- 5.2 Investigation - Geometric Effects of Complex Arithmetic
- 5.2 Practice - Complex Graphing - Practice
- Blank Graphs - 4 Blank Graphs on a single page

Lesson 3: Complex Multiplication
- 5.3 Investigation - The Geometric Effect of Complex Multiplication
- 5.3 Practice - Complex Multiplication - Practice

Lesson 4: Distance and Midpoint Formulae
- 5.4 Investigation - Distance on the Complex Plane
- 5.4 Practice - Distance and Midpoint Formulae - Practice

Lesson 5: Polar Form and DeMoivre’s Theorem
- 5.5 Investigation - Polar Form and DeMoivre’s Theorem
- 5.5 Practice - DeMoivre’s Theorem - Practice

Lesson 6: More Complex Multiplication
- 5.6 Investigation - Discovering the Geometric Effects of More Complex Multiplication
- 5.6 Practice - More Complex Multiplication - Practice

Lesson 7: Polynomial Roots, Revised
- 5.7 Investigation - Polynomial Roots, Revised
- 5.7 Practice - Polynomial Roots - Practice

Lesson 8: The Fundamental Theorem of Algebra
- 5.8 Investigation - Does Every Complex Number Have a Root?
- 5.8 Practice - Fundamental Theorem - Practice

Lesson 9: The Binomial Theorem
- 5.9 Investigation - The Binomial Theorem/li>
- 5.9 Practice - Binomial Theorem - Practice https://youtu.be/iOQjV0FB9nY
- Video - Binomial Theorem - Nancy Pi video

Assessments

UPA 1 - Complex Treasure Hunt
UPA 2 - Fractals

Resources - Matrices

The following are links to resources for Complex Numbers:

Entire Unit - Coming Soon

Complex Numbers - Entire unit on Khan Academy

The following are other free resources:

GeoGebra - Free online math tools

Desmos - Free online graphing calculator

Questions, Comments and Concerns

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