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 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...
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...