Sophia Learning
Sophia: Simplifying Complex Fractions in the Real World
This lesson provides real world examples that involve simplifying complex fractions. Students can watch a video tutorial and then take an online quiz.
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: Intro to Complex Analysis: Basic Complex Analysis
In this video lesson students explore complex number by looking at Argand Diagram, magnitude, modulus, argument and exponential form.
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?
Sophia Learning
Sophia: Complex Numbers
Complex numbers are investigated in this video lesson. The tutorial demonstrates how to add, subtract, and multiply with the imaginary number 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]
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.
Khan Academy
Khan Academy: Algebra: Complex Numbers: Introduction to I and Imaginary Numbers
Video introduces i as the imaginary unit, gives two versions of the definition for i, and then shows what various powers of i equal. [5:20]
Study Pug
Study Pug: Complex Numbers and Complex Planes
Watch this video to learn what makes up a complex number, as well as how to plot on a complex plane. [5:45]
Khan Academy
Khan Academy: Absolute Value of Complex Numbers
Sal finds the absolute value of (3-4i).
Khan Academy
Khan Academy: Absolute Value Inequalities Word Problem
Sal solves a word problem about a carpenter by writing an appropriate absolute value inequality and solving it.
Khan Academy
Khan Academy: Absolute Value and Number Lines
One easy way to think of absolute value is the distance it is from zero. To do that, a number line comes in handy. Watch and learn.
Khan Academy
Khan Academy: Absolute Value & Angle of Complex Numbers
Sal finds the modulus (which is the absolute value) and the argument (which is the angle) of a complex number
Khan Academy
Khan Academy: Adding Complex Numbers
Video describing how to add and subtract complex numbers with examples.
Khan Academy
Khan Academy: Complex Numbers Basic Example
The video lesson from Khan Academy provides practice questions for the SAT. Watch Sal work through a basic Complex numbers problem.