About This Chapter
Complex and Imaginary Numbers - Chapter Summary and Learning Objectives
Just when you thought you had math figured out and you thought you knew all the possible numbers in existence, you get the shock of your life. There is such a thing as an imaginary number. You heard that correctly. Imaginary numbers really do exist (as odd as that sounds).
So, what is an imaginary number? If it's imaginary, then how can you see it? What do you even do with a number that's imaginary? Do they have some sort of fairytale-like superpower? Stop fretting! All your questions will be answered once you watch our video lessons. You may be surprised at what you learn. Imaginary numbers are not really scary at all (and, yes, you can see them because they aren't literally imaginary).
Once you have the riddle of imaginary numbers figured out, you can move on. This means learning about complex numbers. Don't let the word 'complex' get you all worked up, either. It doesn't mean difficult. You'll learn what a complex number is and how to work with these numbers in addition, subtraction, multiplication and division problems. Our lessons also introduce you to graphing complex numbers and solving quadratics with complex numbers.
Some math topics can be a bit intimidating, but they don't have to be. As you'll see, our video lessons break things down and make them simple to understand. You'll soon figure out that odd mathematical concepts, like imaginary numbers and complex numbers, are really not too bad. So, what are you waiting for? Start watching now!
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 102: College Mathematics course
- Math Foundations
- Linear Equations
- Solving and Graphing Inequalities
- Graphing and Factoring Quadratic Equations
- Properties of Exponents
- Properties of Polynomials
- Simplifying and Solving Rational Expressions
- Properties of Functions
- Logarithms and Exponential Equations
- Probability and Statistics
- Studying for Math 102