I received a question on one of my Youtube video posts on the Casio Fx991 scientific calculator asking if it was possible to do complex number calculations on this calculator. The answer is of course yes – which then prompted me to make a quick video today on exactly how to do that with the fx991. See the video below:

This of course then made me think of our other technologies and that perhaps I should show how to do complex numbers with these tools as well.

Here’s the steps on the graphing calculators (any of the Casio models, since they all basically work similarly – the beauty of Casio, the buttons are relatively consistent). This example uses the CG50, but see fx-9750, fx-9860, etc).

And finally, on ClassPad.net, the FREE online math software that does it all – statistics, geometry, graphing, and of course calculations. (You can sign up for a free account (ALWAYS free) – here’s a quick how-to).

The question of course arises, when are we even using complex numbers? Or why do we need them? As I never really taught math content that required students to utilize complex numbers, I don’t feel I am able to answer these questions with authority, so I did a bit of research. For one, if we just go from a ‘content/standards’ perspective, if you are in states that incorporate The Common Core Math Standards (or a version of, whether renamed or not), then it is actually part of the High School: Number and Quantity standards which state, “Students will…”:

Perform arithmetic operations with complex numbers

Represent complex numbers and their operations on the complex plane

Use complex numbers in polynomial identities and equations

But, that of course doesn’t really get at why do we need them. So here are some things I found in my search for this answer. I admit I can’t explain these any more than just listing them, but it at least points to places where complex numbers are in fact important and needed.

Complex numbers are used in electronics to describe the circuit elements (voltage across the current) with a single complex number z=V+iI

Electromagnetic fields are best described by a single complex number

People who use complex numbers in their daily work are electrical engineers, electronic circuit designers, and anyone who needs to solve differential equations.

Hopefully this is helpful to those of you who are in fact doing complex calculations for whatever reason!

Here at Casio we have had enough. Enough excuses. Enough misinformation. Enough hearing “we use TI calculators in our school” or “I don’t know how to use a Casio calculator” or “my students are coming to class with Casio calculators and I don’t know how to help them”. So, this year at NCTM in San Francisco, we decided to challenge TI calculator users to a face-off with Casio in order to show, face-to-face, head-on, that Casio calculators are MORE intuitive, easier-to-use, more efficient and beautiful, and let’s face it – MORE AFFORDABLE! And if the crowds at the booth weren’t evidence enough of the fun everyone was having, and if the gasps from the audience (filled largely with TI-calculator users and some TI-exhibitors too) didn’t make it clear that Casio has a superior calculator, then perhaps some pictures and videos are needed!

We had 10 Face-Off challenges throughout the entire NCTM conference – with an average of about 3 games per challenge, so that’s about 30 games where Casio Prizm faced-off against the TI-84+ CE. And – Casio won EVERY SINGLE TIME – hands down, no contest. There were 12 activities to choose from, and the TI-volunteer contestant was allowed to spin and choose the activity for each game (and some of them got creative, let me tell you!) You naysayers reading this might claim the games were rigged – that we picked activities where TI had no chance. However – we picked 12 common mathematical activities that most high-school algebra/algebra II students would be expected to do with any calculator:

Find the intersection (s) of two graphed functions (a linear & quadratic)

Find the root (s) of a graphed quadratic function (on the graph)

Find the min/max of a given function (on the graph)

Graph y= and r= functions ON THE SAME GRAPH

Graph a vertical line (not draw – GRAPH so we can find coordinate points)

Find the area of intersection between two graphed functions (show on graph)

Find the intersection (s) of two graph functions (cubic and trigonometric)

Find the root (s) of a cubic on the graph of the function

Make a Box Plot and Find the 1-variable statistics from a given set of data

Graph two inequalities and show their intersection on the graph

Given a function (quadratic), find x-value for a given y-value, and find y-value for a given x-value

Casio just does these better – faster, more efficient and you don’t have to hunt around for which menu to use or ask, “do I use the “test” or the “math” button to go to the next step?”, and you don’t waste time tracing and guessing. A more efficient, faster processing calculator does not mean the contest is rigged – it just means the calculator is better. It’s the calculator – not the problems!

Yes, yes – you TI users out there, there are probably mathematical calculations that a TI might be able to do quicker or the same as a Casio. But, what was very apparent, in every single challenge with every single TI-contestant (s) (many times they had to work with a partner), was that even experienced users of the TI cannot always remember what buttons to push, where the menus/operations are that they need, what the steps are, what to turn on or off. It was a process….sometimes a long process….and it was obvious, even with half the people in the audience helping, that using a TI graphing calculator is confusing, with a lot of steps that are often hidden. As everyone could see (and as our Casio teacher contestants, Jennifer N. Morris,Tom Beatini, and Mike Reiners, explained while we waited for the TI folks to finish), the Casio graphing calculators have the menus/tests/processes you need right on the screen, easily accessible, making getting to the next step more efficient, intuitive, and not a mystery or scavenger hunt. And – the graphs on the Casio display faster and the points/intersection or calculations you need stay on the screen – you don’t have to redo anything or write it down before moving on to the next.

The point of the game was obviously to show the Casio/TI difference. Our bigger goal was to open the minds of TI-users, who often use a TI because “it’s what our school/district buys” or “it’s all I know”. I think we succeeded in our goal – we had many converts to Casio during our NCTM Face-off Challenge – hard not to be a TI-to-Casio convert when the difference is right there in front of you. In fact, two of our TI-contestants took off their TI t-shirts and replaced them with Casio Prizm t-shirts during the game (we only caught the second on film unfortunately) to show their new-found appreciation for the Casio. They “saw the light through Prizm” as the shirt says. For those of you that weren’t there, all we ask is that you stop settling for the status-quo and what you’ve always done and make a change.

Take me – in my 25 years of teaching, I used a TI for 20 of those years. I would never go back to a TI now that I have used a Casio calculator. Even after 20 years teaching with a TI, I still can’t remember where to find things – and what steps to follow. When I tried to learn the TI-Navigator – I was so frustrated and irritated that I stopped trying and just used the 84-face plate. With Casio – it took just a short time to get use to the interface, as it is different from TI – but after that initial familiarization with the menu and buttons, I don’t forget how to do anything because it’s all there in front of me, on the screen, no matter which menu I am in. Truth be told, all our Casio teacher-trainers are former TI users – and none of them would go back. Casio is just that much better.

Alright – I’m listening. I am hearing some negativity.

I hear some of you saying that calculators are going away, and we will all be using web products and apps. And – while schools are slowly becoming more 1:1 and mobile apps and web-based calculators might be showing up more in classrooms, the fact is that 67% of students DO NOT have regular access to mobile technology on a regular basis. But calculators are in the hands of 83% of today’s students. With funding in education continually diminishing, and access and equity to technology a major issue, for the foreseeable future, calculators are an inexpensive way to get technology into the hands of ALL students. Students are buying calculators, and more and more are buying Casio’s because they are more affordable (you can get a Casio graphing calculator for about half the cost of a TI-graphing calculator), and easier for them to learn. Calculators are here for a long while still, so let’s get some hand-held technology into the hands of students now so they can explore mathematics instead of waiting for the one day a week, or month, they might get to use that lap-top/tablet cart or go to the computer lab.

Check out some of our videos showing the Casio vs. TI difference. There will be more to come. Explore some of our free online resources that will support you and your students learning of the Casio calculators, especially those of you who have so many students bringing in their Casio’s to class. Why not take a free, self-paced online Prizm course and get a free Casio Prizm Emulator to use in your classroom? Casio is definitely the more affordable way to go with better functionality. Be a convert!