About This Chapter
Who's it for?
This unit of our High School Algebra I Homeschool course will benefit any student who is trying to learn about operations using imaginary and complex numbers. There is no faster or easier way to learn about imaginary numbers. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn how to add, subtract, divide or multiply complex numbers.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need an algebra curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and an imaginary numbers unit exam confirm understanding or identify any topics that require review.
Imaginary Numbers Unit Objectives:
- Learn the processes for adding, subtracting and multiplying complex numbers.
- Find out the steps needed to divide complex numbers.
- Discover how to graph a complex number on the complex plane.
- Learn to solve quadratics with complex numbers as the solution.
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 within the High School Algebra I: Homeschool Curriculum course
- Basic Arithmetic Review: Homeschool Curriculum
- Solving Math Word Problems: Homeschool Curriculum
- Decimals & Fractions: Homeschool Curriculum
- Percent Notation: Homeschool Curriculum
- Working with Real Numbers: Homeschool Curriculum
- Exponents & Exponential Expressions: Homeschool Curriculum
- Simplifying Square Roots: Homeschool Curriculum
- Algebraic Expressions & Equations: Homeschool Curriculum
- Composing Functions: Homeschool Curriculum
- Matrices & Absolute Value: Homeschool Curriculum
- Working With Inequalities: Homeschool Curriculum
- Properties of Exponents: Homeschool Curriculum
- Algebraic Distribution: Homeschool Curriculum
- Writing Linear Equations: Homeschool Curriculum
- Factoring in Algebra: Homeschool Curriculum
- Graphing & Factoring Quadratic Equations: Homeschool Curriculum
- Properties of Polynomial Functions: Homeschool Curriculum
- Rational Expressions & Equations: Homeschool Curriculum
- Cubic Equations: Homeschool Curriculum
- Solving Quadratics: Homeschool Curriculum
- Measurement & Geometry: Homeschool Curriculum
- Percent & Proportions: Homeschool Curriculum
- Data, Statistics & Probability: Homeschool Curriculum
- Well-Known Equations: Homeschool Curriculum