i and Imaginary numbers

[captainLAGER]

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?

[Bbfromthehood69]

thank you i finally understand the trick behind imaginary numbers!!!!!! :D

[ruggjess]

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

[avi0500]

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

[waynemv]

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]

@waynemv 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.)

[me31192]

anyway thanks a lot teacher

[me31192]

Hard!

[acousticisforbitches]

@kyranhymas

You distinguish it simply by ignoring that it can be divided by 2.

It's all based off of multiples of 4. (if it isn't divisible by 4 like "26" then that's where the 4 + comes in. i^26 = -1

Ignore the 2!

[VegitoBlitz24]

Chuck Norris can find the square root of a negative number.

[123waybad]

@VegitoBlitz24 get over chuck norris already you fuckin loser

[VegitoBlitz24]

@123waybad Funny... just noticed your icon has a piece of shit on it. Must be a real life representation of your face.

[123waybad]

@VegitoBlitz24 no its yours

[MattyHild]

@123waybad

Amazing.. Keep the mind-numbing arguments to cat videos, please.

[123waybad]

@MattyHild lol fuck you if it numbs ur mind dont read them dumbass. i bet you can't even learn complex numbers

[mike88189]

thank god for you or i wouldnt be able to sleep in algebra class

[waleedsrahmatullah]

A number within a number. Integerception.

[RiddimPirate]

man, thanks a lot. for real, i have a shit long term sub in my college math 1 class, and you are the only reason i am able to pass. please keep making videos, your a fucking hero to me. idk, you explain the same thing as everyone else, but you do it in a way i can inderstand, and after watching your videos it seems simple.

[CJJLyou]

But waht is i to the 504 power?

[ben1996123]

@CJJLyou

1

[Ecdub984]

@CJJLyou 504 / 4 is 126 so 1

[MilitaryMan006]

OK then what is i to the power of half (square root of i), what is the cube root of i etc. can you define the fractional powers of i? what is i to the power of 3/4? In order to answer these questions I tried to graph i^x = y on a number plane, I ended up with a wave like graph you would find for a trigonometric function. i^1=i which = 0 on the number plane. These numbers are too 'imaginary'

[sqgl]

Sometimes you use x symbol sometimes you use a dot. Maybe add an annotation for the beginners to let them know what is going on? Good stuff to pass on to my non-maths friends otherwise.

[RayOchoa232]

9 people got their brain blow by imaginary numbers and missed the like button



[cjmitz]

@RayOchoa232 1 person didnt miss the like button and just disliked your stupid comment trying to get lots of thumbs up

[YuiiAmemiya]

Super !

I just learnt intro on complex no today :D

I love your calculation :D

What about i to the power of infinity ?

Or to the power of any fraction ?

[jh3835]

ah man thanx for this video. my professor has this on the test and i didnt get it.

he had.....i^246= -1 since 246 divided by 4 has a remainder of 2 which is i^2= -1. easy thanx again.

[honchell12]

i think the proper grammar would be imaginary numbers and i.

[AlexDuude]

You must be reeeallly good at first person shooters

[bandet888]

Anything to the FIRST power NOT ZERO is equil to itself. Anything to the zero power is equil to zero

[MrAthos3]

@bandet888 No, it isn't. Do you remember your old exponent rules?

[bandet888]

@MrAthos3 Not exactly. What is anything to the power of zero equil to? I Know that anything to the power of one equils itself - I think. Like 2 to the power of 1 is equil to 2 - right?

[TheDescendantOfChaos]

@bandet888

Let n be a real number.

Then, n^1= n and,

n^0= 1

[iGuessImABeast]

This puts the 'i' in 'Inception'.

[MsMomoMania]

Thank you! Like the philosophical briefs :D

[dudeB15]

I love his metaphysical moments :)

[sevichp]

At 4:19, you say "i to the negative one power equals i" when you should say "i to the first one power equals i".

[J21C412D0]

but 100 and 500 are divisible by 2 also...

[givemericht]

Very good, now let's go QUANTUMMMMMMMMMMMMM

[krraa]

Philosophy playlist? I think so!

[88joeana]

great presentation! :)

keep the good work up sal!

[Rookycastle22]

can you teach modulo

[bobbinator37]

i^-4= 1/i^4=1/1=1, it works!

[lxdannydxl100]

A number times the same number is a negative. WE MUST GO DEEPER.

[TheYontartu]

@lxdannydxl100 im not saying it's aliens, but its aliens.

[hahs4]

sal was down in this video =(

[pantyflash]

Like, just imagine: The i's have it. "i" just can't handle the power. Good God, babe!

[100CommonCents]

@khanacademy

You should get a Pad, or touchscreen where you can write more clearly. i would expect your subscribers would increase, and probably pay for itself.

just saying. i still love these vids. keep it up/

[MrFloydc2]

you have not done a tutorial on modulus,

please do it for us ?

[Ralzaly]

4:32 its like he just discovered that hahaha

[southflorida14]

a number squared does not equal a number cubed. therefore i does not exist

[MarvelsofaLifetime]

“a number squared does not equal a number cubed. therefore i does not exist.” 1^2 does not equal 1^3, therefore i does not exist. Nice proof.

[kvn89]

@MarvelsofaLifetime 1^2 does not equal 1^3? yes it does. They both equal 1

[MarvelsofaLifetime]

@kvn89 Lol, moron, I was using an example to point out your flawed logic. Here’s what you said: “a number squared does not equal a number cubed. therefore i does not exist” I was just pointing out that your assertion is false with that example.

[punkistz]

@southflorida14 1^2=1^3 :)

[southflorida14]

i does not exist because no number squared equals a negative number. 2 positive and 2 negative numbers equal a positive number. so no i does not exist

[MarvelsofaLifetime]

It’s weird, if you think about it, how could raising any number to the power of the zero be equal to one. That’s fucking crazy. If you multiply any number by zero, you get zero; but if you raise any number to the power of zero, you get one. Ahh, the Universe is so hard to understand!

[filmmetoo]

Reading this helped me understand

betterexplained(dot)com/articl­es/a-visual-intuitive-guide-to­-imaginary-numbers/

[ch4nl3r]

WHAT IS AIIIIIIIIIIIIIIIIIIIIIIIIIIIII­IIIIIIIIIIIIIIIIIIIIIIR!?!?!?!­?!?!?!?!?!?!?!?!?!?!?!

:O

[trfan18]

i love imaginary numbers :)

[dannyp136]

Is i^infinity undefined?

[Ep1cRainbow]

You have replaced my Honors Algebra 3-4 teacher. I LOVE YOU.

[titotito666]

Very nice series! Thank you.

[robinrox1]

I left my mouse on the screen and thought the dude in the vid had two mice. tripped me out

[TheUsual1234]

haha wow you just blew my mind :)

[Unsatisfiedchik]

What a Professor in one full semester couldn't teach me, you've taught me in less than 5minutes. You're awesome!!!!! :-) This video was beyond helpful. & this stuff isnt as difficult as I thought sheeshhh

[graywishes]

@Unsatisfiedchik ditto

[Illshlapu]

Thank you so much :D

[FER1PMD]

um yes, why isn't this confusing?

[Wonderpoo101]

what the FUCK is going on ?

[Wonderpoo101]

@Wonderpoo101 got it ! thank you so much <3 <3 <3 <3

my teacher sucks. you're awesome!

[dark3nangel]

THANK YOU SO VERY VERY VERYERYRYRYRYRYRY MUCH

[IndustrialKitt3n]

WHYYYYYY do we need i

?!?!?!?!?

[Hellsslave666]

@IndustrialKitt3n

'cuz we wanna express the sqrt of -1!

[IndustrialKitt3n]

@Hellsslave666 but why do we need the square root of -1 :'(

[Hellsslave666]

@IndustrialKitt3n

Now It's getting philosphical....

It's just that a mathematician doesn't like to have something with no solution so he sais: "sqrt-1 = i"

If you are not mathematician or engeneer you'll never need it ;-)

[IndustrialKitt3n]

@Hellsslave666 :) ohhhhh

[SaphiraPorter]

@IndustrialKitt3n we need i so we can understand bo burnham's song "new math"

"... and Santa Clause multiplied by i..."

[SabretoothSnowMan]

What is i to the power of 1 and a half?

This man has well over-explain it, I am not an idoit; give it up!

[SabretoothSnowMan]

What is i to the power of 1 and a half?

[DrFalcon222]

@SabretoothSnowMan It is equal to the third root of squared i (by definition)

[Tenraiden]

mmmMmm delicious math.

[AnimaEpisodes]

would i cubed = -1? since its -1*-1=1*-1

but in the video you put i^3 = -i which if i = -1 so its i^3 = - -1 and a double negative = a posotive? so I^3 = 1 so what is the point of putting -i?

wouldnt that mean that i^2 =-1 and  i^i = i =-1?

[rujtj]

My brains hurt.

Me goes watch porn.

[AeroplaneWings]

interesting

[cchhrriiss825]

i used to be good at this. soona as the summer came, i forgot it :(

[hsktoadftw]

lol does anything exist

[godspeed28]

How I wish I could pause my real math lectures. Khan you're seriously helping me out here, thanks a lot.

[fendermadder]

fuck this

[danwat1234]

@fendermadder give it a chance. 'i' is easy once you get into it

[BlackGypoMagic]

at 4:42 so 1 equals 5?

JUST KIDDING.

[kevluv93]

WHAT NOW THERE ARE IMAGINARY NUMBERS? I was having a hard enough time with real numbers as it is.

[ISO15924]

I loved Sal's getting carried away in this video. I hope he does that video on whether i exists! I know I can read about it elsewhere, but would be entertaining if Mr. Khan can explain it himself.

[samuel1abarza]

You make mathematics a fun thing to do! I'm sure you inspired many mathematicians out there!

[AchillestheLion]

What happens if you raise i to a negative power?

[BACUS666]

@AchillestheLion Do you even know how they work? i^-5 = (1/(i^5)).

[AchillestheLion]

@BACUS666 If I knew would I be asking...

[BACUS666]

@AchillestheLion Basically, it's the same as with a real number. Except i is the base.

[chenxiaozhu123456789]

@AchillestheLion

probably becomes a fraction eg. 1/i^1

I don't know if such thing exist or not though :S

[gw4photo]

Definitely a better explanation than in my text book. However it would be better if the handwriting was more clear. i and 1 look too much the same.

[rzigmu]

Hello! Nice presentation, although I have read that i is not the square root of minus 1. i is just i.

If i were sqrt(-1), then i*i=sqrt(-1)*sqrt(-1)=sqrt((-1­)*(-1))=sqrt(1)=1, so i**2 would be 1 according to the definition.

The only right definition for i is that its square is minus one. One question: how do you calculate a real number to the power of an imaginary number, say 4**2i?

[BACUS666]

@rzigmu

1. The ''sqrt(x)*sqrt(y)=sqrt(x*y)'' property applies only to real numbers, for the reason you stated.

2. You can't say that i^2=-1, but sqrt(-1)!=i. For any number, x and y, if x^2 = y, then x is the square root of y. No exceptions. Learn what you are talking about before you do so.

3. 4^2i would have to deal with trigonometric ratios. I know e^ix = cos(x)+tan(x)i, and doing the same with four instead of e would have a similar yet different process, resulting in with odd numbers.

[amritaraoisthebest]

mujha sumj ayi- sukriya

[Rayden440]

This is some crazy stuff.

[got2livelaughlove]

"i" am confused!!! "i" need to watch this again...so basically, just memorize the pattern and don't misplace the i, -i, and 1? gottit! uhg!

[madiana101]

the habd writting is a little bit confusing

[cutewhosena96]

my own stupid brother know this!

[infoherper]

@cutewhosena96 so then he wouldnt be stupid..

[bacelona2011]

please spped it up to make it perfect!

[omegajak12]

whoa im 12 and in algebra 1 and this is algebra 2 and it was cool..... but its not real its imaginary.......imaginary.....­..not real..... but its real.....i is a number? .........i dont get it.......

[Maxpow33r]

he took the long way @ 2:35, i^4 = i^2 X i^2 = -1X-1 = 1 so everything i^factor of 4 = 1 i^even numbers but not factor of 4 = -1

[jonolollmao]

hey can someone explain where i went wrong

i = √-1

i² = (√-1) ∙ (√-1)

this is in form of (√a) ∙ (√b)

which is the same as √(ab)

i² = √(-1 ∙ -1)

i² = √(1)

so i² = -1 or 1???

[FreezingSun14]

@jonolollmao the property sqrt(a)*sqrt(b)=sqrt(ab) is a property of REAL numbers, not of imaginary ones.

[edwardo44]

@jonolollmao

i² =(-1 ∙ -1) good

i²=√(-1)²

i² =-1

[rzigmu]

@jonolollmao : exactly, I have posted the same thing. The only valid definition of i is that i squared equals negative 1. i IS NOT THE SQUARE ROOT OF NEGATIVE 1.

[RSuelzer]

@jonolollmao The form (√a) ∙ (√b) does not work for imaginary numbers. :) an interesting fact. This is the reason that they use i instead of -1 to prevent this type of confusion.

so (√i) ∙ (√i) is simply i. or √-1

I think that is how it works.

[plokijuhujikolp]

ok gets the: i1000= 1 right?

[plokijuhujikolp]

what if: i1000?

[rinwhr]

3:04 how did he get to i x i? I thought i^4 = -i x i

but -i is -1 and i is sqrt(-1)

- 1 x (sqrt(-1))? Where did he get the second sqrt(-1) from?

[trashmail8]

Really recommended: Google for:

"A Visual, Intuitive Guide to Imaginary Numbers" for a very nice and clear article at BetterExplained.

This awesome video + that visual guide == first understanding of imaginary numbers after years of trying! :-)

5 stars for all khanacademy videos too! :-D

[loveandanarchy1111]

Imaginary Numbers are so cool!

[onlyAerik]

Thanks for reminding us to come back to this video when talking about the maclauren series.

[baseballkid077]

Salman Khan for president

[sameeehh]

thanks mate . tons of help.

[idster7]

i would like to hear you philosophically muse, and say why i is useful to engineers and physicists.

[baseballkid077]

my math teacher told our class that (i) is pointless. he said the only time that (i) was ever used was when hawking and them were trying to find the origin of the universe or something..

[LitheonAV]

Imaginary numbers are used with real numbers for complex numbers, and complex numbers are used in quite a few different areas such as engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory.

[IMBLUESTREAK23]

Math kicks ass!!

[momiji920]

So apparently 4 is like god in imaginary numbers. XD

[idster7]

@momiji920 how so?

[BuddhistmeansWisdom]

Visualizing Imaginary Numbers:

There is an unrevealed major breakthrough! No Bluff!

Imaginary Numbers are no more confusing!

How would you value such indepth understandings?

Nothing is free to be shared... Make a genuine offer!

Welcome to the new generation of Mathematics!

Able and interest, will contribute with sponsorship. Spread the word...

Thank you.

Reply to: grlm_bandara@yahoo.co.uk (Mr. Lakshan Bandara)

[davidrodgersNJ]

Now I'm wondering about "e to the i pi equals -1." What's all that about? Anyone?

[TeamFortressKilla]

Euler's equation

[ColloidalWarrior]

@davidrodgersNJ ; "e to the i pi" thing is euler's formula, its a way of representing real and imaginary numbers as one number... It's been a while since I've done this but you want to find out then look up euler's formula.

[patilnikh]

Science and Maths is all about deriving, no wonder every vscience/math video that

I see is just derived from, substituting...

I just hope every engineer must be tired of deriving this.. substituting that....

[8cccpeevostokzempf]

What a Great GREAT Teacher irrspective of the subject.

[theimaginarynumber]

i and -i are equal to the square root of -1. Everyone forgets my brother.

[karlkarlkarl1234]

I can see how all of this is done, but I can't even begin to imagine any applications that it may be useful for in engineering & physics? I'm a newbie engineer student though.... :(

[Tys0nFawlay]

appearently its useful if you study electricity on a higher level, dont know how though

[maxymyllyon]

communications, radio and satellites use this.

[bcpmax]

what dose exiest? do i exist ? could this all be a dream? What is existing?

[chi94]

@bcpmax dunno why dnt u test your totem

[gmfrederik]

@bcpmax shut up

[zMaGna720z]

@bcpmax As far as you know, only you exist. It could be all a "dream"; scientists could have your brain in a vat and be stimulating your brain in such a way that you appear to be doing the things that you are doing, when, in fact, you are really not. However, you can be certain that you exist. After all, if you didn't exist, what would you say is doing all of the "dreaming" or "thinking"? Of course predicates such as thought must have a subject, and that subject is you. Congratulations!

[TaiwanRule]

@bcpmax an A is an A

you existed alright :D

[Forman6]

@bcpmax

existing in the 3rd dimension

[amjPeace]

I love how you finished by saying "I hope you have fun!" because yes, I am having fun!

[infidelguy]

Thank you for this video. However, you didn't really explain, "why" i equals the sqr rt of -1.

[lafilafi]

an imaginary square root of a number is not a number but a set of two numbers

sqrt9 dos not equal 3i but {3i,-3i}

the third imaginary root i a set of three numbers...and so on..

peace

[lukewarmocha]

Blows my mind. Haha thanks for this.

[marzto]

Thanks for making this video.

[Touge1211]

what a bunch of jack asses, Hes making it a Great explanation n taking his time so if a 5 year old wants to learn this he could understand....so if u know good STFU n let the people that dont know learn,,,,,

[nugg69]

OMG GET ON WITH IT LOLOLOL

[ryan23933]

math is useless bullshit

[dekekyo]

mr.Khan.......have a coffee(please) thank you for the explanation.....Imaginary neg. 1 is a conundrum....harder than figuring out what to buy the man who has everything!!!

[atatatr]

ur a fag

[BornInAsphodelMeadow]

I don't know the directed audience of this, but at the point of learning I was at when I learned this, you could have explained it to me in about 2 or 3 minutes, a lot of this video was slow and redundant. If it's directed towards a less academic crowd, I understand but damn, I just kept thinking "I get it, move on". It would have been cool if you'd told us more about what the uses for i are.

[WishofDeath666]

Anyone seen the Robot Chicken sketch on i?

[Mahhbadd]

My brain is fried.

[ninetails009]

If its an imaginary number, then why in the world are we takling about it?

LOL

[oldgitseangraham]

one got very bored did one

[lisinka3]

Somewhere I read that i is the square root of any negative number, is that true?

[syredeathtrooper]

yeah generally 'i' or iota is numerically supposed to be equal to the under-root of -1..since its -1 and not any other number underneath the root, you can take it common from any square root of any kind of negative number (since 1 is common among all possible numbers)

[Selendomono]

i is used to EXPRESS the square route of a negative number. like the square route of -25 can be expressed as the square route of positive 25*square route of -1 (i) so the answer to the square route of -25 is 5i. So i is used to express square routes of negative numbers

[marzto]

No, sqrt6 would be 6i and so on.

[marzto]

oops, my mistake.

sqrt-9 would be sqrt9 x sqrt-1

so sqrt9 is 3 and sqrt-1 is i

sooo answer is 3i