Ch 9: Complex and Imaginary Numbers: Help and Review
About This Chapter
Who's it for?
Anyone who needs help learning or mastering college preparatory math material will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:
- Have fallen behind in understanding imaginary numbers or how to work with complex numbers.
- Need an efficient way to learn about complex and imaginary numbers.
- Learn best with engaging auditory and visual tools.
- Struggle with learning disabilities or learning differences, including autism and ADHD.
- Experience difficulty understanding your teachers.
- Missed class time and need to catch up.
- Can't access extra math learning resources at school.
How it works:
- Start at the beginning, or identify the topics that you need help with.
- Watch and learn from fun videos, reviewing as needed.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Submit questions to one of our instructors for personalized support if you need extra help.
- Verify you're ready by completing the Complex and Imaginary Numbers chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Complex and Imaginary Numbers chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any relevant question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- What is an imaginary number?
- How do I add, subtract, multiply and divide complex numbers?
- What steps and terms do I need to know to graph a complex number?
- How do I use imaginary numbers to solve quadratic equations?
1. What is an Imaginary Number?
An imaginary number is a complex number that results from the square root of a negative number. Find out where the concept of imaginary numbers came from, and learn how to solve problems involving complex numbers and imaginary numbers.
2. How to Add, Subtract and Multiply Complex Numbers
Complex numbers are a combination of a real number and an imaginary number that follow rules similar to those for regular numbers. Learn how to add, subtract, multiply and divide complex numbers through demonstrations of each.
3. How to Divide Complex Numbers
Complex numbers are composed of both real and imaginary numbers and are capable of being divided using conjugates comprised of two binomials that are identical apart from the sign on the second term. Learn more about the definition of conjugates and how to divide complex numbers using complex conjugates and multiplying conjugates.
4. How to Graph a Complex Number on the Complex Plane
Complex numbers can be graphed, but use a different system to identify their coordinates that functions similarly to real number graphs. Learn how complex numbers are represented on complex axes and planes as a point on a graph.
5. How to Solve Quadratics with Complex Numbers as the Solution
Quadratics, even those with complex number solutions, can be solved using the discriminant, and square roots. Practice this with polynomials, and isolate the variables to solve the equations.
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Other Chapters
Other chapters within the College Preparatory Mathematics: Help and Review course
- Math Foundations: Help and Review
- Problem Solving & Reasoning Skills
- Percents in Math Basics
- Decimals & Fractions Overview
- Understanding Fractions & Mixed Numbers
- Linear Equations: Help and Review
- Solving and Graphing Inequalities: Help and Review
- Graphing and Factoring Quadratic Equations: Help and Review
- Properties of Exponents: Help and Review
- Praxis I Math: Square Roots
- Properties of Polynomial Functions: Help and Review
- Simplifying and Solving Rational Expressions: Help and Review
- Praxis I Math: Algebraic Expressions
- Properties of Functions: Help and Review
- Logarithms and Exponential Equations: Help and Review
- Data & Estimation
- Logic in Math: Help and Review
- Sets: Help and Review
- Basic Probability and Statistics: Help and Review
- Praxis I Math: Basic Statistics and Probability
- Geometric Laws & Proofs
- Grade Level Math Vocabulary: Help and Review
- MTEL Middle School Math/Science: History of Geometry
- MTEL Middle School Math/Science: Geometric Properties & Theorems
- MTEL Middle School Math/Science: Principles of Geometry
- MTEL Middle School Math/Science: Algebraic Applications in Geometry
- MTEL Middle School Math/Science: Using Trigonometric Functions
- MTEL Middle School Math/Science: Trigonometric Identities
- MTEL Middle School Math/Science: Trigonometric Applications
- Praxis I Math: Ratio and Proportions
- Praxis I Math: Congruence and Similarity
- Praxis I Math: Geometric Measurement and Dimension