Khan Academy
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...
Khan Academy
Introduction to i and Imaginary Numbers, Imaginary and Complex Numbers, Precalculus
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.
Khan Academy
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...
Khan Academy
IIT JEE Complex Numbers (Part 1), Imaginary and Complex Numbers, Precalculus
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 shows how to divide two complex numbers but runs out of time and continues in the...
Khan Academy
Introduction to I and Imaginary Numbers, Imaginary and Complex Numbers, Precalculus
Students are always fascinated by imaginary numbers. In this video, Sal defines the imaginary unit, i, and shows that it has a cyclic nature when raising i to an exponent.
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...
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...
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 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...
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...
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...
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...
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...
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 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...
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...
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...
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
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...
Khan Academy
Khan Academy: Algebra: Complex Numbers: Complex Numbers (Part 1)
Video first reviews what imaginary and complex numbers are. Shows example of graphing a complex number. Gives general explanations and formulas for adding, subtracting, multiplying and dividing complex numbers. Includes link to...
Khan Academy
Khan Academy: Algebra: Complex Numbers: Iit Jee Complex Numbers (Part 1)
Video shows working a problem from the IIT JEE test which involves using algebraic manipulation to determine the validity of an equation with magnitudes of the differences of certain complex numbers. [7:21]
Khan Academy
Khan Academy: Intro to Complex Number Conjugates
An instructional video describing complex conjugates. Complex conjugates are defined and then used to simplify a problem in which a complex number is divided by another complex number. [8:03]