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 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...
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 Determinant Example
Sal solves a complex determinant problem from the 2010 IIT entrance test. Knowledge of determinants, the exponential form of complex numbers, trigonometric ratios, and algebraic thinking are all utilized here.
Krista King Math
Complex Fractions
Complex fractions are fractions divided by fractions—complicated, right? The video introduces the class to algebraic complex fractions. With the introduction to variables in the denominator, it is important make sure the denominator is...
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
Complex Numbers - Multiplying and Dividing
Algebra In action! Watch the step-by-step process needed to multiply and divide complex numbers. The FOIL method is used to solve two different practice problems involving multiplication and multiplying by the conjugation is used to...
Curated OER
How Do You Graph Complex Numbers?
Complex numbers have two parts and can be graphed on a complex plane. After an explanation of the complex plane, this video shows three examples of graphing complex numbers.
3Blue1Brown
Cross Products | Essence of Linear Algebra, Chapter 8
Equate the area of a parallelogram with the magnitude. The 11th installment in a 15-video series introduces the concept of the cross product of two vectors. The presentation makes the geometric connection between the cross product, the...
Curated OER
What's a Complex Expression with Rational Expressions?
The teacher defines a complex fraction. She writes an example on the whiteboard. She says that any fraction that additionally has another fraction in either the numerator, or the denominator, or both, is a complex fraction.
Curated OER
How Do You Solve a Word Problem That Compares Two Complex Fractions?
Fractions, money, and a word problem? Write out an equation that has a fraction as the numerator of a fraction. Huh? Confusing? Don't give up! Watch the video as the instructor illustrates and explains how to solve this seemingly...
Curated OER
How Do You Solve a Quadratic Equation with Complex Solutions by Completing the Square?
The quadratic equation x2,3,4x + 5 = 0 is solved by completing the square in this video. Two complex solutions are found and are checked in the original equation to verify that they are solutions.
Curated OER
How Do You Find the Least Common Denominator of Two Rational Expressions?
Adding fractions that are in rational expression form? Do they have a common denominator? No? Well, then the least common denominator needs to be found. How is the least common denominator of rational expression found? Watch this video...
Curated OER
How Do You Add Complex Numbers by Graphing in the Complex Plane?
Graphs usually add an extra dimension to ones understanding of mathematical concepts and graphing complex numbers is no exception. This video shows to graph complex numbers on the complex plane and what the results of adding complex...
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,...
Curated OER
Compound Interest and e (Part 2)
Sal continues to look at changing the length of compounding time, from daily to hourly compounding interest. Now he is able to show that compounding 100% annual interest converges on the number 2.71É or e as the number of compounding...
Curated OER
Compound Interest and e (Part 3)
Continuing with the lesson on compound interest, in this video, Sal derives the general formula for any amount of principle, interest rate, and compounding periods over one year.
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.
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...
Curated OER
How Do You Turn a More Complicated Expression into Words?
Given an algebraic expression, write a word problem. Usually it's the other way around where you have a word problem and need to write an algebraic expression. But, this is a good skill to have because it would mean that one has a good...
Curated OER
How Do You Convert a Mixed Expression To a Rational Expression?
Given a monomial and a polynomial, rewrite the expression as a rational number. This is not as confusing as you might think. First is to make the monomial a rational number by giving it a denominator. Once that is done, numbers can be...
Curated OER
Equations And Inequalities
A number of problems involving inequalities and defining the variables are a piece of cake to Sal, and they will be to your Algebra pupils as well after they watch this video. Sal's careful explanation and clear annotations are key to...