About This Chapter
Complex Numbers - Chapter Summary and Learning Objectives
In these lessons taught by math professionals, you'll get details on how to handle complex numbers when you come across them in an algebraic equation. You'll see examples and practice problems, so you get a detailed look at how to do what you've been taught in the lessons. After watching these lessons, you'll understand:
- The differences between complex numbers and imaginary numbers
- How to solve equations using imaginary numbers
- The process needed to divide complex numbers
- Conventions required for graphic complex numbers
- How to determine if your solution is real or complex
|What is an Imaginary Number||Find out where imaginary numbers came from and why they're important. Get the definition for a complex number and details on patterns that emerge when using imaginary numbers.|
|How to Add, Subtract and Multiply Complex Numbers||Find out the formula for adding complex numbers and how to handle the negative signs when subtracting. Examine the different methods you can use to multiply complex numbers. Learn how multiplying complex numbers is similar to multiplying binomials.|
|How to Divide Complex Numbers||Refresh your knowledge of complex conjugates and find out how to multiply conjugates. Determine how conjugates are used to divide complex numbers.|
|How to Graph a Complex Number on the Complex Plane||Find out how a complex number can represent two things and why it's important. Learn about the real and imaginary axis.|
|How to Solve Quadratics with Complex Numbers as the Solution||Learn how the discriminant is used to solve quadratic equations in standard form. Find out how to solve polynomial problems with the 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 within the Math 101: College Algebra course
- Foundations of Linear Equations
- Matrices and Absolute Value
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Exponents and Polynomials
- Rational Expressions
- Radical Expressions & Functions
- Exponentials and Logarithms
- Probability Mechanics
- Sequences and Series
- Studying for Math 101