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]
Khan Academy
Khan Academy: Algebra: Complex Numbers: Iit Jee Complex Numbers (Part 3)
Video shows working a problem from the IIT JEE test which involves determining whether the determinant of a matrix of four given complex numbers is 0. [3:09]
Khan Academy
Khan Academy: Pre Calculus: Basic Complex Analysis
A video [13:04] introducing complex analysis. Complex numbers are defined as a number having two parts: a real part and an imaginary part. The instructor shows how to graph these in the complex number plane. The video also explains how...
Khan Academy
Khan Academy: Pre Calculus: Exponential Form to Find Complex Roots
This video illustrates how the exponential form of a complex number can be helpful in finding the complex roots of a number. The process is shown both algebraically and graphically using x^3 = 1 as a simple example. [11:53]
Khan Academy
Khan Academy: Algebra: Complex Numbers: Iit Jee Complex Numbers (Part 2)
Video shows working a problem from the IIT JEE test which involves algebraic manipulation and using what the argument of complex numbers is to visually reason if two given equations about arguments are true. [7:26]
Khan Academy
Khan Academy: Pre Calculus: Complex Determinant Example
A video showing the step-by-step solution to a difficult determinant problem from the IIT-JEE. This is problem 53 from Paper 1 of the 2010 exam. A 3 X 3 matrix is given in terms of z and omega, where omega is defined as a complex number...
Other
Secc: Hsn cn.c.8: Extend Polynomial Identities to the Complex Numbers
This resource is from the Southeast Comprehensive Center (SECC) at the American Institute for Research which is funded by the U.S. Department of Education. The video explains Common Core Standard HSN-CN.C.8 which states: Extend...
Other
Dimensions
The resource includes two hours of video broken into nine chapters that explores dimensions, complex numbers, and proof. Commentary is available in a variety of languages and background information on the nine chapters is provided.