About This Chapter
How it works:
- Begin your assignment or other college algebra work.
- Identify the imaginary and complex numbers concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.
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This chapter of our College Algebra Tutoring Solution will benefit any student who is trying to learn imaginary and complex numbers and earn better grades. This resource can help students including those who:
- Struggle with understanding imaginary numbers, how to perform basic mathematical functions with complex numbers, how to solve quadratics involving complex numbers or any other imaginary and complex numbers topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their imaginary and complex numbers unit
- Cope with ADD or ADHD
- Want to get ahead in college algebra
- Don't have access to their math teacher outside of class
Why it works:
- Engaging Tutors: We make learning imaginary and complex numbers simple and fun.
- Cost Efficient: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.
- Consistent High Quality: Unlike a live algebra tutor, these video lessons are thoroughly reviewed.
- Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn imaginary and complex numbers on the go!
- Learn at Your Pace: You can pause and rewatch lessons as often as you'd like, until you master the material.
- Define the imaginary number.
- Learn how to add, subtract, multiply and divide complex numbers.
- Examine how to graph a complex number on a complex plane.
- Study how to solve quadratics with complex numbers as the solution.
- Understand how to use the discriminant to tell the kind of solution you will get.
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 College Algebra: Tutoring Solution course
- Overview of Linear Equations: Tutoring Solution
- Solving Matrices and Absolute Value: Tutoring Solution
- Overview of Inequalities: Tutoring Solution
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics: Tutoring Solution
- Working with Exponents and Polynomials: Tutoring Solution
- Identifying and Working with Functions: Tutoring Solution
- Rational Expressions: Tutoring Solution
- Solving Exponentials and Logarithms: Tutoring Solution
- Factorials and Binomial Theorem: Tutoring Solution
- Calculating Sequences and Series: Tutoring Solution