# Ch 5: Complex & Imaginary Numbers: College Math Lesson Plans

### About This Chapter

## Weekly Syllabus

Below is a sample breakdown of the Complex & Imaginary Numbers: College Math 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 | Imaginary numbers | Complex numbers, i and complex conjugate |

Tuesday | Addition, subtraction and multiplication with complex numbers | Formulas for adding and subtracting complex numbers, combining like terms, distributive property and order of operations |

Wednesday | Division with complex numbers | Conjugate and complex conjugate |

Thursday | Graphs of complex numbers | Complex plane, x-axis and y-axis |

Friday | Solutions for quadratics with complex numbers as the solution | Discriminant and zero product property |

### 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 Mathematics Syllabus Resource & Lesson Plans course

- Math Foundations: College Math Lesson Plans
- Linear Equations: College Math Lesson Plans
- Inequalities: College Math Lesson Plans
- Quadratic Equations: College Math Lesson Plans
- Properties of Exponents: College Math Lesson Plans
- Properties of Polynomials: College Math Lesson Plans
- Rational Expressions: College Math Lesson Plans
- Properties of Functions: College Math Lesson Plans
- Logarithms & Exponential Equations: College Math Lesson Plans
- Logic: College Math Lesson Plans
- Sets: College Math Lesson Plans
- Probability & Statistics: College Math Lesson Plans
- Geometry: College Math Lesson Plans