| Titles: | Descriptions: |
| MIT Mathlets | This collection includes the topics: PreCalculus, Calculus and Probability and Statistics. |
| Interactive Math Applications | This collection includes the topics: Graphs, Algebra, Exponential Growth, Matrices, Logarithms, Trigonometry, Complex Numbers, Vectors, Counting, and Calculus. |
| Cut the Knot | This collection includes the topics: Memory and Matching, Logic, Arithmetic, Algebra, Probability, Geometry, and more. |
| About | This collection includes the topics: Geometry, Functions, Trigonometry, Calculus, Statistics and Linear Algebra. |
| Interactive | This collection includes the topics: Algebra, Calculus, Discrete, Fractions, Geometry, Graphs, Modeling, Number and Operations, Probability, Statistics, Trigonometry and more. |
| GeoGebra Applets | This collection includes the topics: Graphs, Precalculus, Calculus, Constructions, Statistics, and more. |
| National Library of Virtual Manipulatives | This collection includes the topics: Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. |
| Titles: | Descriptions: |
| Unit circle | This applet allows you to see the exact values of the degree angle, x coordinate, y coordinate, sine, cosine and the common points. |
| Exact Values | This applet allows you to see the exact values of the degree angle, x coordinate, y coordinate, sine, cosine and tangent of the first quadrant. |
| Trig Ratios | This applet shows the connection between the Unit Circle and Trig Ratios. |
| Radians | This applet shows the Unit Circle in Radians and a visual of how it is measured. |
| Sine & Cosine | It gives a visual aid to see how the graphs sin and cos are related to the x and y coordinates on the unit circle. |
| Cosine Graph | This applet shows the connection to the cosine graph and the unit circle. |
| Sine Graph | This applet shows the connection to the sine graph and the unit circle. |
| Tangent Graph | This applet shows the connection to the tangent graph and the unit circle. |
| Symmetries | This applet shows the symmetries found on the unit circle. |
| Degrees and Radians | This applet shows the transition from degrees to radians on the unit circle. |
| Titles: | Descriptions: |
| Complex number arithmetic and geometry | Algebraic and graphical representations of addition, subtraction, multiplication and division of complex numbers. |
| Complex Arithmetic | Multiplication and Division of complex numbers. |
| Dynamic Link | Detailed description, prompts and an interactive applet on complex numbers. |
| The Mandelbrot Set | This applet explores the Mandelbrot set which exists on the complex plane. |
| Fractals | This applet explores fractals and builds a foundation of knowledge to understand the Mandelbrot set and Julia sets, which are a useful application of complex numbers. |
| Julia Sets | This is an applet the explores Julia sets. |
| Powers of Imaginary Numbers | Describes what the number i is and how to calculate large powers of i. |
| The Complex Number System | A geogebra applet that explores different types of numbers, particularly imaginary and complex. |
| Complex Numbers | An applet that dissects the real and imaginary part of a complex number graphically giving the two demential number a visual representation. |
| Complex Plane | This applet explores the complex plane and how it works. |
| Finding roots of complex numbers | Graphical representation of the roots of complex numbers. |
| Nth roots of Unity | Explores the roots of complex numbers on the unit circle, their angles and a geometrical representation. |
| Euler's Formula | Graphical demonstration of Euler's Formula and how it relates to complex numbers. |
| Transformation of x^2 | This applet shows the transformations of a(x+b)^2+c. |
| Derivative Applet | Discover and graph derivatives of functions. |
| Discovering Parabolas | Relationship between Focus, Directrix and Parabola. |
| Conic Sections | Discover conic sections. |
| Volumes of Solids | An applet that explores the volumes of spheres, cones and cylinders. |
| Upper and Lower Sums | Explore the area under the curve f(x). |
| The Normal Approximation to the Binomial | Explore the cumulative probability of a binomial distribution and how it compares to the normal curve. |
| Roots (Something New) | Explore the roots of the function f(x). (I discovered a new tool on Geogebra with this applet for my something new.) |
| Original Geogebra Applet | A graphical representation of the multiplication of complex numbers. |
| Link | A graphical representation of the addition and subtraction of complex numbers. |
| Worksheet | Activity on graphically representing addition, subtraction and multiplication of complex numbers. |
| Lesson Plan | Lesson Plan describing the activity and how it will run in the classroom. |
| Link | An applet I created to graphically represent the addition and subtraction of complex numbers. |
| Multiplication of Complex Numbers | An applet I created to graphically represent the multiplication of complex numbers. |
| Desmos Applet | Applet that shows the addition, subtraction and multiplication of complex numbers. (This is the applet we actually used for the activity as I didn't have the originals created at the time of the activity.) |
| Encrypted Message | This is a copy of the encrypted message for students to work with. |
| Lesson Plan | Lesson Plan describing the activity and how it will run in the classroom. |
| PowerPoint | Powerpoint presentation on the simple affine cipher. |
| Affine Cipher Applet | An applet Adam created on simple affine cipher. |
| Desmos Activity | An activity I created on Desmos. It reviews inequalities and factoring. It then goes through a step by step process of solving quadratic inequalities. |
Allen, E. S. (1922, September). Discussions: Definitions of Imaginary and Complex Numbers. The American Mathematical Monthly .
Andreescu, T., & Andrica , D. Complex Numbers from A to Z. New York: Birkhäuser.
Asmar N.H., Grafakos L. (2018) Complex Numbers and Functions. In: Complex Analysis with Applications. Undergraduate Texts in Mathematics. Springer, Cham
Dolan, S. (2015, July 15). Complex numbers and triangles. Retrieved from The Mathematical Gazette: https://www.cambridge.org/core/journals/mathematical-gazette/article/complex-numbers-and-triangles/1463449812E013D27B00F263040306C1
Dugoplolski, M. (2007). Trigonometry. New Jearsey: Pearson Education.
Kramer J., von Pippich AM. (2017) The Complex Numbers. In: From Natural Numbers to Quaternions. Springer Undergraduate Mathematics Series. Springer, Cham
Grosholz, E. R. (2013, January). Teaching the Complex Numbers: What History and Philosophy of Mathematics Suggest. Journal of Humanistic Mathematics , 73.
Merino, O. (2006, January). A Short History of Complex Numbers. Retrieved from University of Rode Island : http://www.math.uri.edu/~merino/spring06/mth562/ShortHistoryComplexNumbers2006.pdf
Miller, J., & Gerken, D. (2017). College Algebra (2nd Edition ed.). New York, New York: McGraw Hill Education.
Nahin, P. (1998). An Imaginary Tale: The Story of √ −1. (P. U. Press, Producer) Retrieved from American Mathematical Society: https://www.ams.org/journals/notices/199910/rev-blank.pdf
Neri F. (2019) Complex Numbers and Polynomials. In: Linear Algebra for Computational Sciences and Engineering. Springer, Cham
Nordlander, M. (2011, November). On the concept image of complex numbers. Retrieved from International Journal of Mathematical Education in Science and Technology: https://www.tandfonline.com/doi/full/10.1080/0020739X.2011.633629
Panaoura, A. (2007, Feb). Geometric and algebraic approaches in the concept of complex numbers. Retrieved from International Journal of Mathematical Education in Science and Technology: https://www.tandfonline.com/doi/full/10.1080/00207390600712281
Peters, C. (2018). The Reality of the Complex: The Discovery and Development of Imaginary Numbers. Retrieved from Lee University: http://sigmaa.maa.org/hom/resources/Contests/Peters2018.pdf
Scoville, N. A., & White, D. (2019). An Introduction to the Algebra of Complex Numbers and the Geometry in the Complex Plane. Retrieved from Digital Commons: https://digitalcommons.ursinus.edu/cgi/viewcontent.cgi?article=1002&context=triumphs_complex
Vaught, R., & Rae, A. (2016). Scholar. (S. F. University, Producer) Retrieved from Imaginary numbers: http://sfsu-dspace.calstate.edu/handle/10211.3/173533
Vince J. (2018) Combining Waves Using Complex Numbers. In: Imaginary Mathematics for Computer Science. Springer, Cham
Windred, G. (2016, Nov 03). History of the Theory of Imaginary and Complex Quantities. Retrieved from Cambridge University Press: https://www.jstor.org/stable/3606116?origin=crossref&seq=1#metadata_info_tab_contents
Yager, R. R. (2013, March 04). Pythagorean Membership Grades, Complex Numbers, and Decision Making. Retrieved from International Journal of Intelligent Systems: https://onlinelibrary.wiley.com/doi/full/10.1002/int.21584
Young, C. (2010). Precalculus. Hoboken, New Jersey: John Wiley and Sons .
| Type of Resource: | Links | Description |
| Applet | Link | Experimenting with a complex plane. Understanding addition, subtraction and multiplication graphically. |
| Applet | Link | Complex Numbers A Dynamic Tool |
| Applet | Link | This applet is a graphical demonstration of Euler's formula |
| Applet | Link | Arithmetic Operations with Complex Numbers |
| Applet | Link | Geogebra applet involving imaginary numbers |
| Images | Link | Image descriptions of complex numbers, cartesian plane, adding, subtracting and multiplication. |
| Podcast | Link | Discussion on Imaginary Numbers and understanding the world around us. |
| Podcast | Link | Video podcast describing the properties and uses of imaginary numbers. |
| Video | Link | Imaginary Numbers Are Real Part 1 of 8: Introduction |
| Video | Link | The Real World Uses of Imaginary Numbers |
| Video | Link | Imaginary Number - Sixty Symbols |
| Video | Link | Imaginary Numbers Large Exponents |
| Video | Link | Fundamental Theorem of Algebra - Numberphile |
| Website and Video | Link | A Visual, Intuitive Guide to Imaginary Numbers |
| Website and Video | Link | Interactive website describing the history and origin of the idea of complex numbers. |
| Website | Link | Interactive website eleven sections of interactive technology. |
| Website | Link | Clark University Dave's Short Course on Introduction Complex Numbers |
| Website | Link | Remarks on the History of Complex Numbers and First Geometric Interpretation of Negative and Complex Numbers |
| Website | Link | History, explanation, applet and interactive website by Utah University on the Mandelbrot set. |
| Website | Link | Imaginary numbers, complex numbers, arithmetic and applications. |