Precalculus - Unit Five
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
- Lesson 1: Introduction to Complex Numbers
- Lesson 2: Complex Graphing
- Lesson 3: Complex Multiplication
- Lesson 4: Distance and Midpoint Formulae
- Lesson 5: Polar Form and DeMoivre’s Theorem
- Lesson 6: More Complex Multiplication
- Lesson 7: Polynomial Roots, Revised
- Lesson 8: The Fundamental Theorem of Algebra
- Lesson 9: The Binomial Theorem
- Assessments
Resources - Matrices
The following are links to resources for Complex Numbers:
The following are other free resources:
- GeoGebra - Free online math tools
- Desmos - Free online graphing calculator
Questions, Comments and Concerns
Please free to contact Alyve with any corrections or suggestions.
Also, please contact Alyve if you feel that any of the content is derived from copyrighted material.
Contact Alyve