i and Imaginary numbers

waynemv Says:

Dec 26, 2011 - i^2 = -1, leads to an ambiguity that's often glossed over. That equation has two solutions, as also (-i)^2 = -1. One might ask: Are i and -i the same or different numbers? Do you have students take for granted these are different numbers, or do you actually prove so? Given that -0 = 0, it's not obvious that -i can't be equal to i. Also, any polynomial with all real coefficients that has i for a root also has -i for a root. Is that a mere coincidence? So what's the distinction between i and -i?

waynemv Says:

Dec 26, 2011 - I didn't really express it right above. But, the situation is that i and -i appear to share all the same properties, they are like identical twins. The only distinction between them seems to be that they are not each other - in every other respect they seem interchangeable! (As long as one is consistent and interchanges them everywhere they occur within a problem.)

avi0500 Says:

Jan 13, 2012 - im here exactly for the deeper meaning of i ,not to see what i and the rest of the masses have been taught to do with i, damn it .where can i find the reason for the inception of this weird idea

ruggjess Says:

Jan 23, 2012 - This was very helpful in remembering what my intermediate algebra teacher had taught. I just needed that refresher...this was it! Thank you!!

Bbfromthehood69 Says:

Jan 26, 2012 - thank you i finally understand the trick behind imaginary numbers!!!!!! :D

captainLAGER Says:

Jan 31, 2012 - I am an engineer and wanted to show my girl a video about i, too bad all the stuff you teach in this video is pretty much irrelevant. Who cares about i^543. What about Gauss?

rich1051414 Says:

Feb 23, 2012 - -i and i are both neither negative or positive. i is a special number that cannot be negative or positive therefore the - sign is meaningless when applied simply to i. This is the reason i is so philosophical to many mathematicians. How it is so useful and needed for math yet is not really a number at all, but when two of these non numbers meet, it produces one(or negative 1 rather) :P.

K3NatCSS Says:

Mar 8, 2012 - Around 1:50 I just went "you fucker, quit confusing me more than what's needed and get on with it"

Juliuserver Says:

Apr 4, 2012 - There is no number that multiplied by itself equals -1. How can "i" be an actual number? It does not make any sense...

xloisxisxcoolx Says:

Apr 13, 2012 - You know this guy's good at teaching when you start watching videos totally irrelevant to the course you're studying.

YThursday Says:

Apr 13, 2012 - Yes, because of course all YouTube videos are made specifically towards your needs.

IronAnimation Says:

Apr 14, 2012 - i really wish your i's looked more distinct from yoiur 1's

actionjessie Says:

Apr 24, 2012 - Its for electronics engineering, something to do with a sine wave because it goes up and down in the negative and positive direction so they need to find the square root of a negative number..

actionjessie Says:

Apr 24, 2012 - Are there any videos that will show me how to simplify imaginary numbers in cartesian? e.g 1/(1-i^2) - 1/1+j)^2

Juliuserver Says:

Apr 25, 2012 - Thank you for your comment. I'm going into engineering so I am trying to understand all of these more mysterious concepts in math.

TheAlivePixel Says:

May 9, 2012 - ( i ) Finally understand...

cool80827 Says:

May 9, 2012 - i dont know if im right but i think i is -.5

gabriel youso Says:

May 13, 2012 - im sooooo confused WHHHHHATTTTT R U SAYING

killa12222 Says:

May 15, 2012 - Oh wow, after 2 class lectures and still having no clue, I finally understood after watching this in 10 minutes :D Thanks man!

poisenkake Says:

May 16, 2012 - x^2 + 1 =0 ; x^2 = -1 ; there is no real number such that if you square it, it will give you (-1), in short, the solution can not be a real number.Let us say that i=sqrt(-1) is that solution, so: i^2 + 1 = sqrt(-1)^2 +1 = -1 +1 = 0So, the solution hast to be i = sqrt(-1).If you want another GOOD reason for use of imaginary number, private message me.

macojonesfam Says:

May 16, 2012 - i squared = -1

macojonesfam Says:

May 16, 2012 - simple...kind of

macojonesfam Says:

May 16, 2012 - what grade are you guys in? im in 7th grade!the book "imaginary numbers" inspired me to do math! i love math... and pi!3.14159265358979323846264338327950288419716939937510582097494459230781640628... and so on. i know more but i bet you just read the first few digits:) go math!

TheKurtPrice Says:

May 22, 2012 - But if 100 is a multiple of 4 and equals 1 couldn't it also equal -1 because 100 is a multiple of 2?