Ch 5: Complex Numbers: College Algebra Lesson Plans
About This Chapter
Weekly Syllabus
Below is a sample breakdown of the Complex Numbers chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
| Day | Topics | Key Terms and Concepts Covered |
|---|---|---|
| Monday | What is an Imaginary Number? | The origins of imaginary numbers |
| Tuesday | How to Add, Subtract and Multiply Complex Numbers | The differences between imaginary and complex numbers, and the formulas for adding, subtracting and multiplying complex numbers |
| Wednesday | How to Divide Complex Numbers | The importance of complex conjugates when dividing complex numbers |
| Thursday | How to Graph a Complex Number on the Complex Plane | The process of graphing real and imaginary numbers |
| Friday | How to Solve Quadratics with Complex Numbers as the Solution | Solving quadratics and polynomials with complex and imaginary solutions |
1. What is an Imaginary Number?
The imaginary number 'i' is the square root of -1. Although this number doesn't actually exist, pretending that it does allows us to do a bunch of crazy math that scientists use every day. Learn the basics of that number 'i' here!
2. How to Add, Subtract and Multiply Complex Numbers
Knowing that complex numbers exist is the first step. But that knowledge alone won't help you do much with them. Learn the basics of complex number addition, subtraction and multiplication here!
3. How to Divide Complex Numbers
While adding, subtracting and multiplying complex numbers is pretty straightforward, dividing them can be pretty tricky. It comes down to the process of multiplying by the complex conjugate. Learn about what that is, and how to do it, here.
4. How to Graph a Complex Number on the Complex Plane
Graphing complex numbers is pretty straight forward, but it's not necessarily intuitive. Check out this lesson to learn the vocabulary and the conventions that you'll need.
5. How to Solve Quadratics with Complex Numbers as the Solution
When you solve a quadratic equation with the quadratic formula and get a negative on the inside of the square root, what do you do? The short answer is that you use an imaginary number. For the longer, more helpful answer, check out this lesson!
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Other Chapters
Other chapters within the College Algebra Syllabus Resource & Lesson Plans course
- Foundations & Linear Equations: College Algebra Lesson Plans
- Matrices & Absolute Value: College Algebra Lesson Plans
- Inequalities: College Algebra Lesson Plans
- FOIL, Parabolas & Quadratics: College Algebra Lesson Plans
- Exponents & Polynomials: College Algebra Lesson Plans
- Functions: College Algebra Lesson Plans
- Rational Expressions: College Algebra Lesson Plans
- Exponentials & Logarithms: College Algebra Lesson Plans
- Probability Mechanics: College Algebra Lesson Plans
- Sequences & Series: College Algebra Lesson Plans
