Polynomials and Imaginary Numbers: Study Hall Algebra #8: ASU + Crash Course

Polynomials are incredibly useful - not just for mathematicians, but for anyone trying to model something complicated, like the weather. But there can be so much to keep track of when we're multiplying them, and dividing them can seem impossible. In this episode of Study Hall: Algebra we'll pull out our magnifying glasses and use detective work (and the best method: the box method) to multiply and factor polynomials.
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[@Mushbeary]

7:26 "while these imaginary solutions might not have real world meaning" I believe what he is trying to say is that they do not equate to anything in the physical world, not that they serve no purpose, since any physicist, engineer or computer scientist can tell you otherwise.

[@kiarra.0413]

this was incredibly helpful, tysm

[@arizonastateuniversity]

You are more than welcome! Feel free to explore other videos in this playlist as well: kzbin.info/aero/PLNrrxHpJhC8l8q8cq9BXLS3guOcyLqxj6

[@ScienceCommunicator2001]

Thanks for the much needed info! And I like your Australian accent. But the so-called "imaginary numbers" that you say don't have physical meaning are actually as real as negative numbers. Am doing some personal research and very soon will prove it once and for all!

[@patrickmeehan6856]

7:26 "While these imaginary solutions might not have real world meaning..." And mic drop. This is the ENTIRE reason most people dislike math. It is just so irrelevant. Playing with numbers is fun, but it's just that: playing. It's a game. I love this CC series. I've been sharing it with my public middle school math teacher friends and they're digging it too. Some of the examples from previous videos about real world applications and situations interest both teacher and learner. Please help make imaginary numbers relevant to a middle school boy who is rapidly checking out of math without reverting to "one day in your job you might" or "computer coding and algorithms..." or "if you become an engineer" or other tired and ineffective cliches and responses addressing the question "when am I ever going to use this?"

[@milkdoubt8837]

Hello, I rarely comment in yt but felt an extreme amount of empathy in regards to your comment. I was once there too (quite recently actually) when I kept pondering the "practical" uses of math. But as you will mature and the more you explore the world using different tools such as mathematics, you will soon realize that the "practical aspect" or the "when am I ever going to use this" questions will soon diffuse as you become exposed to the beautiful nature of mathematics. Considering the fact you're still in middle school and already checking out topics such as these already baffles me. As a senior student in highschool, it excites me to know that younger people still retain their curiosity to explore In regards to imaginary numbers, yes they have very practical uses, an example would be in physics where they have the ability to rotate coordinates or rather vectors on the two dimensional plane which is also used alot in animations or rather anything where the concept of rotations are involved. The utility of concepts lies beyond there truth value or how "real" they are. Think of stories, music, video games, the legal system or anything fictional and you will see how things can have an effect regardless of their actual existence. Heres a link to a recent video from another youtube who explains concepts such as these to a highschool level kzbin.info/www/bejne/a4HGoXWtaq2VrdE Note: Even if you don't plan on becoming an engineer, physicist, or any other cliches, I sincerely urge you to treat concepts with an open mind and don't concern yourself too much with it's practical uses :)Terrible teachers can fog the elegance of certain topics by teaching them in a pretentious or simplistic way but I hope you'll be able to see through that and have an idea for the beauty that lies beneath. What matters most is that the stuff you learn adds richness to how you understand the world and appreciation for how this world works. In times of desperation and confusion such as this, the value of appreciation and beauty cannot be overstated.

[@khiyabarrett1459]

He shouldn't have said that, I'm an electronic engineer and imaginary numbers are used all the time. Theres a famous identity called Euler identity that allows you to convert between trigonometric expressions and complex numbers. This allows for the use of complex numbers while solving equations relating to the working of circuits (an AC electrical signal is in the form of a sine wave and thus trigonometry is used when interacting with it). Look up complex impedance and phasors. A large amount of modern technology would not function without the use of complex numbers.

[@derekcook8358]

1. If you are worried about sounding cliche, then that's a problem in itself. Don't worry about that and just be genuine when you say something you know to be true. One reason students don't like to hear that usual stuff about, "You may need this in your career someday" is because no one has given them any reason to think that they are capable of becoming something that impresses them, like a scientist or engineer. 2. Another hurdle when telling them they will need math or science is that they haven't developed a passion to drive them into it yet and they will not until they believe they can achieve something difficult. One way I see teachers taking the sting out of this kind of conversation is to have a set of questions for their students that finds out what kind of career they might honestly enjoy, then present the math and science requirements for that line of work as something they get to do, rather than have to do. If you need any help with that, start by researching on bls.gov. Usually I hear teachers ask things like, "What do you like to do to relax?" And students often reply with stuff like sketching, music, hiking, playing video games, and texting. Try not to roll your eyes at them. All of that hints at what they might enjoy for a career. Then on the teacher's notes there are several example fields for them to suggest and talk briefly about what the students "get to do" to prepare for this career and why. 3. I can't think of many scientific or engineering careers where you won't need this stuff in spades. And seeing as how STEM careers are in quite a desperate demand right now, and have been on the rise for quite some time, it seems very relevant. Honestly, if anyone out there has the slightest interest in STEM, it is not cliche. In fact, mathematical modelling is nearly becoming a requirement for lower level positions or career success in general. 4. There are countless entrepreneurs out there who only succeed because of their ability to take initiative and use mathematical modelling skills to solve their problems and provide a better product or service as a result. Even landscapers with no college degree, only a diploma or just a few classes in mathematical modelling or statistics, have used algebra like what you see in this lesson to better understand the weak points in the industry or tools or methods and address this with marketable results. I believe you can find some of these people by googling "Biotech documentaries." But, the more humble success stories get taken to heart more often, in my observation. This may be because a student is unlikely to relate to that success or identify with someone who's success seems unattainable from their own current position in school. 5. I used to repair textile machines for a living, and while you do not need any skill in maths to become effective at this, I observed an enormous uptick in performance and troubleshooting abilities in those who took lessons to understand the ratios, exponential equations, and breakdowns in the machines' maintenance books. Those who could not understand how to work through this stuff and make adjustments for power, speed, and interpret that to calculate your hourly output, had to pass the job on to electricians and specialists, who would then take up all your chances for overtime and advancement. And that's not even a STEM career, that was just a low paying position where math skills were not required. 6. (Imaginary Solutions) But, if you need to explain to students why imaginary solutions are relevant, then I envy you as you may be dealing with some really bright young minds. In which case it's as simple as looking to calculus, astronomy and the subatomic. There you can find plenty of imaginary solutions and quantum whatsits to inspire them to pursue that area of mathematics further. Talk to them about probability clouds as a nice taster, that's how I was introduced. It's some of the most basic and useful stuff in all of science. Assuming that you are a teacher, I hope all of this helps you to inspire your students. That's a very important part of teaching that is missed out far too often. If they aren't inspired, they stop learning as soon as they leave your class.

[@Dana0113]

Hi Patrick, I'm 23 years old and I study Computer Science. I always thought that math was boring when I was in grade school and felt frustrated just like you. Now I see how math is like the "stupid" words and "ridiculous" wand movements that Harry Potter has to execute to make his incantation work. The fun/practical aspect of math stems from the awe of the magic it creates. Making a machine that can create artificial intelligence is pretty magical to me, but find something YOU think is cool. Read books on the subject that are written in a more vibrant way than the school textbooks you are used to. Science books that are bestsellers are usually a good choice! TED talks are also an excellent way of being introduced to interesting subjects related to math. This may seem like more homework, but if you want to be happy in life, finding something that you are passionate about early is helpful. I'm sorry if this seems like I'm trying to talk to you like you are a little kid. I really do think this way myself, so if it's childish, so be it :)

[@pinklady7184]

The imaginary number (i) is only a shorthand for (-1)^2 that is unsolvable. Try getting the square root of -1. It is impossible and unsolvable. So the imaginary number i was introduced for that reason.

[@tannerhewison2579]

At 3:10 there’s cigarettes in an ash tray in the animation...