About This Chapter
Complex Numbers & Polynomials in Algebra - Chapter Summary
This chapter serves as a fantastic knowledge booster for individuals interested in learning more about complex numbers and polynomials in algebra. Lessons provide in-depth analyses of imaginary numbers, triangle inequality, polynomial identities and the steps involved in solving complex numbers and quadratics. By completing this chapter, you will be able to:
- Define an imaginary number
- Add, subtract, multiply and divide complex numbers
- Graph a complex number on a complex plane
- Solve quadratics with complex numbers as the solution
- Equate two complex numbers and add complex numbers in the complex plane
- Understand the triangle inequality theorem
- Share the meaning of polynomial identities
- Provide the definition of the fundamental theorem of algebra
Navigate the lessons in any sequence you choose and visit them as often as needed to gain full comprehension of complex numbers and polynomials in algebra. Assess your understanding of the lessons you review by taking their quizzes. If you hit a snag and need additional information about any lesson topics, feel free to send your questions to our experts. Enjoy 24/7 access to all resources in this chapter via any smartphone, tablet or computer with an Internet connection.
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!
6. How to Equate Two Complex Numbers
After watching this video lesson, you will know how to equate two complex numbers with each other to solve for two unknown variables. Learn the one simple rule you need to follow to find your answers.
7. How to Add Complex Numbers in the Complex Plane
Watch this video lesson to see how you can use the complex plane to help you add your complex numbers. See how similar this is to the very familiar Cartesian coordinate plane.
8. Modulus in Math: Definition & Examples
A modulus in mathematics has to do with modular arithmetic, also called clock arithmetic. In this lesson, we'll explore the concept of a modulus. Through definition and example, we'll become familiar with what a modulus is and how to work with it.
9. Triangle Inequality: Theorem & Proofs
In this lesson, we will use definitions and proofs to learn what the triangle inequality theorem is, why it works, and how to use it to determine if three given line segments can form a triangle.
10. What Are Polynomial Identities?
Polynomial identities are effective tools for making our work with polynomials much easier. In this lesson, we will define polynomial identities and explore some useful examples.
11. Fundamental Theorem of Algebra: Explanation and Example
In this lesson, you will learn what the Fundamental Theorem of Algebra says. You will also learn how to apply this theorem in determining solutions of polynomial functions.
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Other chapters within the BITSAT Exam - Math: Study Guide & Test Prep course
- Expressions & Reasoning in Math
- Introduction to Quadratics
- Working with Quadratic Functions Overview
- Mathematical Sequences & Series Overview
- Series & Sequences Application
- Exponential Functions & Logarithmic Equations
- Binomial Theorem Overview
- Overview of Matrices & Determinants
- Sets & Relations in Math
- Introduction to Trigonometric Functions
- Trigonometric Identities Overview
- Real World Trigonometric Applications
- Operating with Functions
- Solving Inequalities
- Two-Dimensional Coordinate Geometry
- Straight Lines & Angles in Coordinate Geometry
- Circular Arc & Circles in Coordinate Geometry
- Conic Sections in Coordinate Geometry
- Three-Dimensional Coordinate Geometry
- Limits & Continuity in Differential Calculus
- Calculating Derivatives
- Differentiable Functions & Min-Max Problems
- Differentiability in Integral Calculus
- Overview of Probability in Calculus
- Vectors & Scalars in Math
- Dispersion & Frequency Distributions in Statistics
- Linear Programming & Systems of Equations
- Definite Integrals
- Permutation & Combination
- Mathematical Modeling Overview
- BITSAT Exam - Math Flashcards