Introduction to i and imaginary numbers
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I've learned this three times over in the past two years, and I just sob every time I try. I can't even learn it, I just get a basic understanding enough to put the answers on the paper, and then I let it go. I can't think of a single occupation in which I will ever use this, and there are plenty of other brain stimulating and strengthening things that I can do to build cognitive pathways. I want somebody, anybody to argue why this is a REQUIRED piece of knowledge that I can't graduate without, and why I should suffer the anxiety and stress of trying to understand something that has no applicable value.
I major in math, but I agree with you to a large degree. When you work a job in our society, and the only math you should apply in life is taxes and paying bills, why would you EVER need to know calc or properties of i if said career isn't catered toward a math inclined job? I believe that mathematics courses should stop at 6th grade, unless of course you have a pursuit in math or are gifted. I agree completely. Mathematics isn't necessary in every career.
*dials up khan academy*
Me: Excuse me, may I speak to Mr. Khan? Yes, I'm a student and I'd like o request
that he come as a guest speaker to my pre-calculous class. Why? Oh, because he's
ten times better than any math teacher at my school.
hey sal why not explain complex variable/function by digging a bit deeper. there are other stuff like branch point, branch cut, rieman surface........ all those great stuff that i dont have a complete grasp.
Theirs a better and easier way to understand this. It always repeats the same number over and over. It goes i,-1,-i,1. It doesn't change so i^1 would be i. Then i^2 would be -1. i^3 is -i. Finally i^4 is 1. Then i^5 Or ^6 ot ^7 or ^8 just repeats agian in that order and it keeps going forever
literally what happened to me also last year in exams- when i m really stressed- and have a lot of tests and quizzes i start to get so overwhelmed. And final exams- alwayYs make me get exhausted and burn out. But seeing how you put this comment six months ago- how did u do? Did U do well. And did all your hard work pay off.
Can we please just call the imaginary number nil.
Well.. that'd be a problem... but it's something similar to "Idk if I am true or false" (i)
So, why does ixi = -1? What if the imaginary number is made known, then it wouldn't be i, it wouldn't be -1 if timesd itself..
so what purpose would the -1 answer if you don't need a number that doesn't exist why does it have a value??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????whoa ... that gltch where the comment box is pushed all the way to right of screen haepfsna hagain .,..waaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
You can visualize these numbers on an xy-plane. Say the x-axis represents real numbers and the y-axis represents these imaginary numbers.
i^0 = 1 is the point (1,0) on your xy-plane
i^1 = i is the point (0,1) on your xy-plane (since the y-axis measures these imaginary numbers)
i^2 = -1 is the point (-1,0), and
i^3 = -i is the point (0,-1), and
i^4 = 1 gets us back to (1,0).
Drawing the circle that connects these dots will help you (or someone else reading) understand what goes on between integer exponents.
For instance, i^(0.5) would be on your circle at roughly the point (0.707, 0.707)--geometrically this would get you at a 45 degree angle from the x-axis on your circle.
So i^(0.5) is roughly 0.707 + 0.707i.
Likewise i^(1.5) is roughly -0.707 + 0.707i, and so on.
I just learned about i two days ago in my algebra class, but am still wondering why it exists. My instructor answered my question with "It's just something we memorize" Can someone explain it to me please?
I'm glad to see you explain this in such an approachable way. Surely this topic invites some seriously complicated topics but I feel like you explain it in a way that anyone could understand. Does anyone else feel like this needs to be taught to kids much earlier so that they have more time to sort through the topic and come to terms with it? I tell my younger relatives all the time that they need to be taking calculus in high school, but admittedly I never mention that they need to understand this topic as well. I hope in the coming years we see some real attention given to such an important topic for budding engineers.
+Justin Wheeler Definitely. Phrases like imaginary units and complex numbers are quite intimidating to a layman. Covering them in school even at a basic level might encourage more kids to carry on to study it further.
+Khan Academy Why do you start your lecture about i without introducing the REASON we need i . and that is to rotate points in 2 dimensional space. That's what i is. i is a VERY ELEGANT way to rotate in 2d space. How? You have to be introduced into complex numbers to learn that. That's what i is all about... Nothing spooky, nothing "imaginary".
The whole "imaginary" bullshit is totally wrong. This "number" (which is not even a number) is a sighn (like a road sign) that points 90 degrees in angle and its purpose is to point you 90 degrees into the 2nd dimension.
so 5+4i means... move 5 units in the right direction and 4 units in the upwards direction.
That's what i is... upward directional movement. But because we use the same numbers (5,4) we have to make a way to represent this movement.
So dear Khan Academy, don't confuse people with this imaginary bullshit. Introduce them properly and we will be glad
(and you know what is the saddest thing? If you go to wikipedia page, and search for i. IT DOESN'T TELL YOU THAT! it only tells you all these bullshit, but it doesn't tell you the real purpose of i... why?)
+Quachil Uttaus It's one thing to understand how to work with i, it's another to understand why you work with i.
Teachers often emphasise the "quick" way to derive a term (nX^n-1). But they don't get taught why or how this is. There's barely any mention of first principles or the real world application of differentiation. It can get in the way of the real understanding of math.
Sure you don't need to understand to pass your High School Calculus exam, but when you get to college, the understanding is going to help you a lot.
+CornerrecordZ We can't percieve i. But you don't need to percieve it. You just need to apply rules of algebra to it and it'll all be fine. Why were you so hung up on what i is? Of course your shitty teachers didn't help, but I'm honestly not curious at all about perceiving i.
Peace out, nigga.
1st my comment is a mess, I apologise for that :/ but anyway, I believe that students need to know what i is, or at least how it can be used, where it is usefull to us. Otherwise they will get confused. I can still remember the confusion that I had when I was introduced in imaginary and complex numbers back in highschool because I was looking for answeres and nobody seem to have them. All I was getting was, " look buddy, this is what it is and if you dont like it, we dont care" basicaly...
students need to be introduced to imaginary numbers in a way that they understand what they are. And if my comment doesnt cover what imaginary numbers then this video should have covered that in the 1st place...
dose this system only work in the decimal system? would it look different in the dozenal system? and if so, what about any number of number systems
I'm really curious but not smart enough to work it out myself
This makes no sense. Dumbest thing I've ever seen. Why not just tell us what the number is? Or at lest tell us what #'s it's in between? If you can't, mabe it's all just in your head; intellectual masturbation.....
The imaginary unit is used to solve for imaginary zeroes in polynomial functions. It is very useful in engineering, astrophysics, computing, and physics. You only discredit it because of its name, "Imaginary." It makes perfect sense, and it applies to much of maths, like in Euler's Formula. Just because you don't understand it, that doesn't make it the dumbest thing ever. It just shows you inability to understand.
anyone know the difference between numbers and operations on numbers?
definition of i contrary to the laws of logic. it is stupid that set of number and
operation on this number, is equivalent to number.
by the same logic we can define j^2=-2 and ect. then the life of "scientists" will become much more difficult. Who has defined this nonsense? - nobody knows
Something about this just seems wrong. I understand that this concept is applied to electricity. I guess the logic is that electrons can't create matter i.e you can't get more than 1 or -1. Yet, didn't the Large Hadron Collider disprove this? A vacuum can create matter, because energy is required to create a vacuum.
Ugh im such a loser, i dont get this, but im not giving up!
although im sorry this video still makes no sense i may need to refer to other resources, i feel left behind -.-
but like i said, Im not giving up
If you could just give an example of a fractional power. Is it like i^(3/2)?
Okay that means first imagine a stick rotated 3 times by 90 degrees. 90 *3 = 270. Now imagine the stick stopped at midway of this 270 degree rotation. 270/2= 135. Thus i^(3/2) = rotation by 135 degrees.
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