Flipped Math
Quadratic Formula
The quadratic formula is what works—always. Instruct your classes on the application of the quadratic formula using a thorough video lesson followed by provided practice problems. The lesson connects algebraic solutions to graphical...
Krista King Math
Completing the Square with Complex Roots
Explore completing the square as a process for finding complex roots of quadratic equations with a video lesson that pulls together several concepts related to quadratic equations. The example shows how to complete the square with a...
Khan Academy
Khan Academy: Algebra: Complex Numbers: Complex Numbers (Part 2)
Video shows how to divide complex numbers by using complex conjugates in general terms and then with a specific example. [8:58]
Khan Academy
Khan Academy: Algebra: Complex Numbers: Complex Numbers (Part 1)
Video first reviews what imaginary and complex numbers are. Shows example of graphing a complex number. Gives general explanations and formulas for adding, subtracting, multiplying and dividing complex numbers. Includes link to...
Khan Academy
Khan Academy: Intro to Complex Number Conjugates
An instructional video describing complex conjugates. Complex conjugates are defined and then used to simplify a problem in which a complex number is divided by another complex number. [8:03]
Khan Academy
Khan Academy: Pre Calculus: Exponential Form to Find Complex Roots
This video illustrates how the exponential form of a complex number can be helpful in finding the complex roots of a number. The process is shown both algebraically and graphically using x^3 = 1 as a simple example. [11:53]
Khan Academy
Khan Academy: Algebra: Complex Numbers: Adding Complex Numbers
Video shows an example of adding complex numbers. Includes link to additional practice problems. [1:11]
Khan Academy
Khan Academy: Algebra: Complex Numbers: Complex Roots From the Quadratic Formula
Video shows how to use the quadratic formula to find roots of a quadratic equation in a situation where the roots are complex. Includes showing how to verify the answers are correct solutions of the quadratic. [10:15]
Khan Academy
Khan Academy: Algebra: Complex Numbers 2
Students learn about complex numbers. The resource examines how to divide complex numbers and complex conjugates. The video tutorial investigates the mathematics concept through detailed notes and examples.
Khan Academy
Khan Academy: Algebra: Complex Numbers 1
Students learn about complex numbers. The resource examines how to add, subtract, and multiply complex numbers. The video tutorial investigates the mathematics concept through detailed notes and examples.
Khan Academy
Khan Academy: Complex Numbers: Complex Numbers (Part 1)
Introduction to complex numbers. Adding, subtracting and multiplying complex numbers.
Khan Academy
Khan Academy: Algebra: Complex Numbers
Video explains what complex numbers are and shows how to write them. Includes an example of writing a real number as a complex number. [2:21]
Khan Academy
Khan Academy: Complex Roots of the Characteristic Equations 2
What happens when the characteristic equation has complex roots?
Khan Academy
Khan Academy: Intro to Complex Analysis: Exponential Form to Find Complex Roots
In this video lesson students learn to use exponential form to find complex roots.
Khan Academy
Khan Academy: Repeated Roots of the Characteristic Equation
What happens when the characteristic equation only has 1 repeated root?
Khan Academy
Khan Academy: Algebra: Complex Numbers: Imaginary Roots of Negative Numbers
Video shows how to simplify the square root of a negative number using the imaginary unit i. [4:04]
Khan Academy
Khan Academy: The Imaginary Unit I: Imaginary Roots of Negative Numbers
Video shows how to simplify the square root of a negative number using the imaginary unit i.
Khan Academy
Khan Academy: Complex Numbers: Complex Numbers (Part 2)
Dividing complex numbers. Complex conjugates.
Randy Thomas
Solving Quadratic Equations With Complex Solutions
This tutorial discusses solving quadratic equations using square roots, completing the square, and the quadratic formula. Problems which previously had no solution can now be solved with the inclusion of the complex number system....
University of New South Wales (Australia)
Unsw: How to Solve Polynomial Equations Involving Complex Numbers
The instructor in this video demonstrates how to use the polar form of a complex number to solve a polynomial equation. [11:07]
Virtual Nerd
Virtual Nerd: How Do You Multiply Pure Imaginary Numbers?
This tutorial demonstrates the steps to find the product of pure imaginary numbers. [5:23]
Khan Academy
Khan Academy: Complex Roots of the Characteristic Equations 3
Complex and repeated roots of characteristic equation.
Khan Academy
Khan Academy: Repeated Roots of the Characteristic Equations Part 2
An example where we use initial conditions to solve a repeated-roots differential equation.