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...
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.
Curated OER
Complex Numbers - Algebra Help
The foil method had been used for years as a way to remember how to simplify complex numbers. This process is demonstrated step-by-step, slowly so the learner will be able to follow along as the instructor solves the problem. Intended...
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...
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.
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 —...
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...
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,...
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
Basic Complex Analysis
This video gives an excellent overview of the different representations of a complex number. First, Sal reviews a pictorial representation of a complex number as an Argand diagram, then shows how to find the modulus and the argument of a...
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...
Curated OER
How Do You Simplify a Fraction Over a Whole Number?
Learn how to take a complex fraction and use the reciprocal rule of division to simplify the fraction.
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