Imaginary Numbers Aren’t Pretend.
Here is the link for my visualization.
When I started this project, I knew that it would be
difficult to take what many people refer to as imaginary and represent it in a
format that made sense. The concept of complex numbers is taught in Algebra 2. Common
Core standards recommend
Represent complex
numbers on the complex plane in rectangular and polar form (including real and
imaginary numbers), and explain why the rectangular and polar forms of a given
complex number represent the same number”
To me, this standard seems less than ideal. There are many high school
students who successfully complete mathematics without a solid understanding of
what complex numbers are, and why they are critical to mathematics. My own informal survey showed that often
times students only knew complex numbers had “something to do with the square
root of -1.”
This is a topic that I am passionate about. Modern
computer graphics to render the images that appear 3 dimensional require
vectors using complex numbers. Computing
the emulates artificial intelligence relies upon complex numbers. MRI imaging
technology requires complex numbers. If our students think that complex numbers
are just make believe, they will not be able to keep up in highly technical
fields.
My target audience is high school students who are currently in or have
completed Algebra 2. I also wanted to make the presentation helpful for all of
the people who (like me a few years back) think that complex numbers are
imaginary and unimportant.
Presenting the information in a graphical way
was very challenging for me. I spent quite a bit of time on Mathematica and Wolfram
Alpha, but I wasn’t able to make the visual representation clear. Ultimately, I
used a graphic that had been designed by Welsh Labs
Initially, I wanted to
demonstrate the complex plane with intersecting circles. By using a parabola
instead, the mathematics was more straight forward. The process of recording the information was where
I learned the most in this project. Each slide walks the student through the
process of visualizing the complex plane. Initially, I was making the
entire thing too complicated. Because the software strongly encourages each
recording to be less than ten seconds, I had to rephrase each point and trim it
down until it was as simple as I could make it.
I think that makes the presentation better. Initially I was confusing
the audience with too much information.
4 comments:
Very interesting topic! I also enjoyed your reasoning behind it. In your writing you also stated you struggled with some of the graphing aspects, which is good as it will help you understand areas your students might have issues as well. Great job!
I like that title, that they are not pretend. I think that is a flaw in the phrase imaginary numbers is that students think they don't exist or something. I really liked how you explained it using more of a 3 dimensional model, I think that one diagram that shows how they actually do cross through the x axis, really made a lot of sense to me. It would be cool to see more of how quadratics interact with that 3rd dimension as we move from real to complex solutions. Overall I really liked how it was a nice introduction toward engaging with the topic.
Hello Karen,
This is the first time that I've saw a visualization as such where the "y axis" imaginary numbers are presented in a 3d model coming towards the viewer (Mind Blown). Thanks for taking your time to explain this in a way that is understandable, and at a pace that is way to stack on track.
Hi Karen,
I absolutely love your video! I have never had someone explain and show imaginary numbers like this and it helped my brain out so much! It's such a good way to explain that they are not pretend, they exist somewhere, you just might not have seen where yet. The visuals in the video supported my need for visual learning and the image at the very end was especially helpful. Great work!
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