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: Multiplying Binomials With Radicals
Video demonstrates how to multiply two polynomials when each polynomial contains one variable term and one radical (constant) term. [6:03]
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: Complex Roots of the Characteristic Equations 2
What happens when the characteristic equation has 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]
Sophia Learning
Sophia: Decartes' Rule of Signs
Determine the number of real roots of a given polynomial function using Decartes' rule of signs. Assess learning with a quiz.
Khan Academy
Khan Academy: Complex Roots of the Characteristic Equations 3
Complex and repeated roots of characteristic equation.
Khan Academy
Khan Academy: Polynomial Basics: Adding and Subtracting Polynomials 1
This video demonstrates how to add trinomials.
Khan Academy
Khan Academy: Algebra: Complex Conjugates Example
Video shows how to write the conjugate of a complex number. Also discusses uses of the complex conjugate and shows an example of multiplying complex conjugates. [4:01]
Khan Academy
Khan Academy: Quadratic Odds and Ends: Introduction to the Quadratic Equation
The video demonstrates how to use the quadratic equation to solve second degree polynomials.
Khan Academy
Khan Academy: Algebra: Factoring Sum of Cubes
Video demonstrates how to recognize and factor a sum of cubes. [4:46]
Khan Academy
Khan Academy: Precalculus: Imaginary and Complex Numbers: Basic Complex Analysis
This Khan Academy video lesson provides a concrete way to help students represent and visualize complex numbers. An Argand Diagram, magnitude, modulus, argument, and exponential forms are utilized in the lesson.
Sophia Learning
Sophia: Finding a Polynomial Passing Through a Point: Lesson 3
This lesson uses the linear factorization theorem to find a particular function polynomial passing through a point given the zeros of that function. It is 3 of 7 in the series titled "Finding A Polynomial Passing Through A Point."
