Curated OER
Complex Numbers (Part 1)
In this video, a complex number is defined and graphed on the complex plane. Sal also shows how to add, subtract, and multiply two complex numbers. He starts showing how to divide two complex numbers, but runs out of time and continues...
Curated OER
Complex Numbers (Part 2)
This video continues looking at dividing complex numbers by looking at the conjugate of a complex number. The instructor then uses the conjugate to rationalize the denominator of a rational expression with a complex number in the...
Curated OER
Complex Numbers (Part 2)
This video continues looking at dividing complex numbers by looking at the conjugate of a complex number. The instructor then uses the conjugate to rationalize the denominator of a rational expression with a complex number in the...
Curated OER
Complex Numbers (Part 1)
In this video, a complex number is defined and graphed on the complex plane. Sal also shows how to add, subtract, and multiply two complex numbers. He starts showing how to divide two complex numbers, but runs out of time and continues...
Curated OER
Complex Conjugates
Sal discusses the usefulness of the conjugate of the complex number is this video. First, he shows both graphically and algebraically adding a complex number and its conjugate. Then, he shows how to simplify a rational expression with...
Welch Labs
Imaginary Numbers Are Real (Part 6: The Complex Plane)
How do addition and subtraction work on the complex plane? A short video presentation provides a clue on how to add complex numbers geometrically. The video ends with four problems to determine the rules for multiplication on the complex...
Welch Labs
Imaginary Numbers Are Real (Part 4: Bombelli's Solution)
Is the square root of negative one crucial to the process of finding other solutions? Using the properties of the newly discovered square root of negative one, historical mathematician Bobelli is able to solve Cardan's problem. His...
Welch Labs
Imaginary Numbers Are Real (Part 3: Cardan's Problem)
Were complex numbers discovered or invented? A video presentation makes the case for the discovery of square roots of negative one. In order for complex numbers to be real, then they must behave like other numbers, which they do in terms...
Welch Labs
Imaginary Numbers Are Real (Part 9: Closure)
The last video in a series about imaginary numbers demonstrates the need for complex numbers. Math pupils learn that they need to include the square root of negative one, the building block of the complex numbers, to have a set of...
Welch Labs
Imaginary Numbers Are Real (Part 5: Numbers are Two Dimensional)
If the square root of negative one exists, where is it on the number line? A math video presents a geometric representation of complex numbers and the complex plane, and then compares it to the geometric representation of real numbers —...
Curated OER
How Do You Multiply Complex Numbers Using FOIL?
How do you multiply complex numbers? The instructor in this video uses the FOIL method of multiplying binomials to multiply two complex numbers. She finishes the problem, by using prior knowledge of the definition of the imaginary unit,...
Flipped Math
Complex Numbers
Simplify the complex with a thorough video lesson. Individuals view a lesson on complex numbers and then use a provided set of practice problems to show what they've learned. The lesson includes instruction on using the four basic...
Welch Labs
Imaginary Numbers Are Real (Part 7: Complex Multiplication)
Multiplying complex numbers geometrically is complicated. Find an easier way with a short video that explains the process of multiplying complex numbers on the complex plane. The connection with the process and the angles and moduli sets...
Curated OER
Introduction to I and Imaginary numbers
Students are always fascinated by imaginary numbers. In this video, Sal defines the imaginary unit, i, and shows when raising i to an exponent it has a cyclic nature.
Curated OER
Introduction to I and Imaginary numbers
Students are always fascinated by imaginary numbers. In this video, Sal defines the imaginary unit, i, and shows when raising i to an exponent it has a cyclic nature.
Curated OER
Exponential Form to Find Complex Roots
Sal solves the problem x^3 = 1 for all of the real and complex roots using the exponential form of the complex number. He shows how the roots found in exponential form are the same as those in a more traditional form of a complex number...
Welch Labs
Imaginary Numbers Are Real (Part 8: Math Wizardry)
How does the Fundamental Theorem of Algebra apply to equations with complex roots? Using recently learned concepts about the complex plane, learners determine all the complex roots of polynomials. They can find the same roots as...
Welch Labs
Imaginary Numbers Are Real (Part 1: Introduction)
What are imaginary numbers? An introductory video provides an explanation as to why we need imaginary numbers to solve equations, and makes the connection between the need for zero, negative numbers, and rational numbers throughout history.
Flipped Math
Imaginary Numbers
Leave nothing to the imagination! Learners view a thorough lesson on imaginary numbers that introduces the concept, shows how to simplify square roots of negative numbers, and then how to solve quadratic equations with imaginary...
Welch Labs
Imaginary Numbers Are Real (Part 2: A Little History)
In some cases, a square root of a negative number must exist in order to determine the roots of a cubic equation. An educational presentation provides a specific example of a cubic with a known root to have an understanding of a square...
Krista King Math
Imaginary Numbers
Scholars learn to use their imagination in math class! The tutorial explains the origin of the number i and then simplifies expressions that include imaginary numbers. The examples include i raised to different powers, giving viewers...
Virtual Nerd
How Do You Find Higher Powers of i?
What is i raised to the 45th power? This video shows you how to break up the problem into a number of i raised to 4th power, and calculate what power is left over to calculate.
Krista King Math
Rationalize an Imaginary Denominator with Conjugate Method
Explore a procedure for rationalizing a denominator that includes imaginary terms with a video that shows how to use a conjugate when working with fractions. The narrator explains the process from start to finish with each step shown in...
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...