This notation and formula is used in quantum mechanics and wave function. Amazingly beautiful. The mathematics euler invented three centuries ago, is now used in an elegant physics theory like quantum mechanics.
@@theadel8591 No. Math is a construct based on provable assumptions. It is definitely an invention. Math does not "exist", it merely describes relations in the physical world.
@@ThefamousMrcroissant saying Math wasn't existent before scientists knew it is completely nonsensical and a child would laugh at such a idea. Math is always there either we discover it or not because without it you wouldn't talk, walk, laugh, cry, think etc. basically everything in the world behaves according to God's laws(if you're an atheist forget I said that to avoid long arguments) that were put before we existed.
@@theadel8591 Throwing ad hominem and a temper tantrum isn't a very sound argument. You should really learn to control that if you wish to have intelligent people respect you at all. Math is a human construct. Math does not "exist"(not in physical reality at least). It is a language of describing relations in physical reality. These relations we try to capture exist, but math itself does not. It's like describing a rock in a book, a rock exists, but the construct "rock" itself is merely a tool to depict the actual object. Thus math isn't "discovered", it is constructed and therefore invented. Another anecdote is that most apes can count, but only to a certain degree and show no ability to multiply. This implies that indeed they have an intrinsic knack for abstraction, but haven't developed it(factoring in this case).
Wowsers, I just heard terms that made so much more sense (just having been exposed to Calc over the past 9 years). Amazing explanations as I have been struggling to fully grasp the why of this formula. Thank you.
Alternatively simply recall that the cartesian coordinate representing the complex value of cosx+jsinx is a point on the unit circle and then use pythagoras' theorem to obtain that same result. (I definitely did not come up with this( ͡° ͜ʖ ͡°))
@@OfficialOffsideBall Anything multiplied by 1 or -1 gives you what you have already started with. Look closely and you will see a notation change. Look at the equation where it says -(-1) And so he multiple sin with -1 making it -(-sin) and then distribute the negative sign and you will get just sinx
Dear Khan Academy, Can you please put a link to the video giving the proof of the euler equation which you referenced in this video. Thank you Appreciate it.
KHAN ACADEMY E U L E R S F O R M U L E A Just watched yr above video. Liked the video and learnt EULERS FORMULA and associated formulas to keep in mind. Clearly audible and clearly visible even in my small mobile screen. CLEAR with out a doubt. Thanks Vatsa BANGALORE INDIA
Perfectly Good Canoe This is just way of transforming them into e, literally just that. Its useful when you are stuck while doing integrals that are difficult.
This equation is obviously wrong. Left side is the exp function which gives values from 1 to infinity. Right side is the sum of 2 trig functions and each gives values from -1 to 1. How can these sides be equal?
Duarte Silva this video is geared toward electrical engineering. It's standard for EEs to use j instead of i for imaginary numbers since i is already used to represent current.
It is called i not j .... i , say it with me, i , they use i for (i)maginary notice that i in there? I know it is not imaginary but most people call it that and they named it after that so yeah use it as is
This notation and formula is used in quantum mechanics and wave function. Amazingly beautiful. The mathematics euler invented three centuries ago, is now used in an elegant physics theory like quantum mechanics.
it's sad that many non-math-lovers keep asking why such mathematicians keep discovery these useless equations (they said)
Math isn’t invented, it gets discovered is the true phrase
@@theadel8591 No. Math is a construct based on provable assumptions. It is definitely an invention. Math does not "exist", it merely describes relations in the physical world.
@@ThefamousMrcroissant saying Math wasn't existent before scientists knew it is completely nonsensical and a child would laugh at such a idea. Math is always there either we discover it or not because without it you wouldn't talk, walk, laugh, cry, think etc. basically everything in the world behaves according to God's laws(if you're an atheist forget I said that to avoid long arguments) that were put before we existed.
@@theadel8591 Throwing ad hominem and a temper tantrum isn't a very sound argument. You should really learn to control that if you wish to have intelligent people respect you at all.
Math is a human construct. Math does not "exist"(not in physical reality at least). It is a language of describing relations in physical reality. These relations we try to capture exist, but math itself does not. It's like describing a rock in a book, a rock exists, but the construct "rock" itself is merely a tool to depict the actual object. Thus math isn't "discovered", it is constructed and therefore invented.
Another anecdote is that most apes can count, but only to a certain degree and show no ability to multiply. This implies that indeed they have an intrinsic knack for abstraction, but haven't developed it(factoring in this case).
Ah yes, oiler
Leon Hard EU Ler & Oi Clid
Who
We have Eular but call him a mechanic✨
Good old oiler
German people are still figuring out how to make good names
🤣🤣🤣🤣good ol’ oiler
Wowsers, I just heard terms that made so much more sense (just having been exposed to Calc over the past 9 years). Amazing explanations as I have been struggling to fully grasp the why of this formula. Thank you.
we love e
don't forget them sinusoids
Yee!
E meme doe
Cringe doe
E
Prove that ( in Euler's formula),
sin^2(x) + cos^2(x) = 1
Solution:-
We know that,
e^(ix) = cosx + isinx........(1)
e^(-ix) = cosx - isinx........(2)
[ 'i' is the complex number]
Then multiply both equations,
e^(ix-ix) = (cosx + isinx)(cosx - isinx)
or, e^0 = (cosx)^2 - (isinx)^2
or, 1 = (cosx)^2 - (i^2)(sinx)^2
[As, (i^2) = -1]
So, 1= (cosx)^2 - (-1)(sinx)^2
or, 1= (cosx)^2 + (sinx)^2
Thus, sin^2(x) + cos^2(x) = 1
(Proved)................. 😁😁😁
Alternatively simply recall that the cartesian coordinate representing the complex value of cosx+jsinx is a point on the unit circle and then use pythagoras' theorem to obtain that same result. (I definitely did not come up with this( ͡° ͜ʖ ͡°))
bro i am dumb. but, how did that (-1) disappear in that 2nd last line?
@@OfficialOffsideBall
Anything multiplied by 1 or -1 gives you what you have already started with. Look closely and you will see a notation change.
Look at the equation where it says -(-1)
And so he multiple sin with -1 making it -(-sin) and then distribute the negative sign and you will get just sinx
@@OfficialOffsideBall
No you are not dumb. You can do this bro.
Such a huge fan of Khan Academy.
Why do electrical engineers use j instead of i as the immaginary unit?
In engineering "i" is used for current, so they use "j" for imaginary numbers.
@@ahmadsagvan3328 thanks
thank you! Eulers formula is mentioned within my matlab class so i just wanted to learn a bit more. Thank you once again!
Dear Khan Academy,
Can you please put a link to the video giving the proof of the euler equation which you referenced in this video.
Thank you
Appreciate it.
And if we let j=1+0i as 1 is an complex number, we get the definitions of hyperbolic trigonometric functions, it all finally makes sense
wonderful explanation
After seeing this, I’m now chasing my football career. What is all this.
we love e
Electricity
@@dominicstewart-guido7598 interesting that there’s applications of this
I actually understood this. ayy I'm going to be doing this in 3 months time...
No 1 cares
@@SauceGodGaming i did, keep your opinions to yourself
@@SauceGodGaming i do
I'm a simple man, I hear "we love e", I hit like
Felling of great achievement after watching this video
WOW! Great quick video...very well presented and explained! Videos of this quality help me fill in the gaps in my math background. ❤ 😊
KHAN ACADEMY
E U L E R S F O R M U L E A
Just watched yr above video. Liked the video and learnt EULERS FORMULA and associated formulas to keep in mind.
Clearly audible and clearly visible even in my small mobile screen.
CLEAR with out a doubt.
Thanks
Vatsa BANGALORE INDIA
we love "E"
The way you teach is damn awesome.....
Yeah I love e too..........
same bro same
we all love e
Sooo helpful!
Sometimes I feel like professors are just gatekeepers... Thank you for the video!
Some professors may not grasp how to relate the information in an idealistic and feasible manner. Dumb it down for us normies like this video!
I prefer the taylor's series proof of this. Then it makes more sense, instead of wondering "how the F does a cosine = an e ? "
I feel like Sal's voice changed
Max Han lol it’s not sal 😂
his name is willy, at least that is what the video says
Start at 3:02 for beginning
Thanks 💪💪
I understood very well thanks sir !
how?
Thank you sir, this is very clear.
I want to drop out of college
Does anyone have a link to the video with the proof for Euler's formula?
a lot on TH-cam
Before seeing this video I love X but now I love E ❤️😅
3:22 thank me later
Max Jakobsson thanks
Thank you
Thank you
Thanks
What video? could you link it?
This is beautiful ..
When i heard Euler I knew I shouldn’t be here, Still in Algebra 2!! Don’t mind me!
Japanese u are
i know this is a old comment, but how was algebra 2, im starting it now?
Thank you sir nice video
where is the Sal's video that proves Euler's formula?
What playlist is this on Khan Academy? And I never heard this teacher before. Who is he?
Thank you Sir
You are not Sal
rude much?
Imposter
no we r only here for sal
@@Snoopy23134 Then you must be stupid😌😑
i feel hes better than sal :P
I did this in high school, it's always fun to watch something you know about.
I can totally relate, I remember doing this in elementary school, it was so much fun
Francisco Villacis same here, good times in pre k
My parents used to feed me this during breakfast. Good times
Hajar Rashidi Did this while being prepared to be in my mother ' s womb. Really great times those were.
ahh good times then doing this while dinosaurs are still around.
You must mean "we love e^x".
but that still works out to e
you mispelt the word
Elegant because it's simple
why are there ten thousand internet explanations of this same thing, but nobody anywhere explains where r x e raised to i theta comes from ???
reminds me of those 'E' memes
"thats the rhythm" baby...
What does j represent? Sorry I'm new to this formula.
Is this essentially putting trig functions in terms of complex hyperbolic trig functions?
Perfectly Good Canoe This is just way of transforming them into e, literally just that. Its useful when you are stuck while doing integrals that are difficult.
Why does that weird morgue guy call this the “soul equation?”
mother fcka is true mathmatecian. He was so lazy to record again so he just wrote over his own notes later xD (only work they do is with the brain.)
I love e.
We love **E**
This equation is obviously wrong. Left side is the exp function which gives values from 1 to infinity. Right side is the sum of 2 trig functions and each gives values from -1 to 1. How can these sides be equal?
Soo simple...❤️❤️
you know that's the German pronounce of the name Euler. I should know I am a Euler after all
But why can't we use planck's constant to this formula?
Why does he say j instead of i?
Duarte Silva this video is geared toward electrical engineering. It's standard for EEs to use j instead of i for imaginary numbers since i is already used to represent current.
@@beefbobjones Thanks for the explanation.
Who's making this video LoL we love you
Ok I think I‘m not getting it. Why is (e^ix+e^-ix)/2 =cos(x) and (e^x+e^-x)/2=cosh(x)
I guess I don‘t understand the difference between e^x and e^ix
This only works for x=0. Exampel e^(pi/4) is not √2.
As cos(π/4) + sin(π/4) = √2.
Try it in a calculator they are not the samme!
I cant wait for the day I dont need to know this anymore
Maybe also interesting the book: Euler’s Formula and Special Relativity: The Deep Origin of Space and Time by Dr. Thomas Stark
What would happen if you had z= cosx + j^2sinx?
real number
if u get -ve angla,u'll have to use -ve sign.
Sabbir Ahmed okay 👍
Would z(e^i•pi) = re^i•pi
Be the a way to write the reciprocal of
z = (R, theta)?
yes.
Sabbir Ahmed thank you for all your help. I really appreciate it. Very nice of you to take the time to reply
It's 2:22 why am I down this rabbit hole?
Me coming here after reading The Earth is Online:
Snake Euler and the math acrobatic team!
Who's this guy...
Willy billy Milly Tilly khilly dilly
i=j?
Be worried Euler, you are getting a copyright by markiplier
this is useful how?
calculus 2
Finding roots to cubic equations
It gets used a lot in a differential equations class
We love e
This is when the meme was born
E 2018 meme was here
are you the guy from black pill
This is easy I was doing Newton 5 th law of biononimal differtiaion I'm the products form
0:14 e meme, anyone?
e
does .5! enumerate?
R J 5! Means 5 factorial. This means 5 times 4 times 3 times 2 times 1.
@@restitutororbis964 He said .5. As in 1/2.
still, so much missing - dunno' how i know - just know
Civic braniac
No, the voice feels totally wrong to me.
what grade is this for?
Depends on the person. Complete algebra, analytical trig and geometry then that person should be ready for this.
iviewthetube I asked grade wise not person wise
I'm in grade 12 and I take this in Algebra II
Ahh ok
Its based on your level of understanding. Nothing to do with grade.
anyone coming from monogatari?
Sir plz putt up bsc pcm chapterwis syllabus in this aap plz in Hindi sir
God bro
Good brother
ahhhhhhhhhh i get it thanks
Hhhhh . it's i not j
Abbas Uday ssss
E
We love you too hahahahaha
wat sê jy?
understood nothing udfghdhrbg
heh, Willy
0:17
❤❤🎉🎉
WASTE OF TIME !!!!! NOT A GOOD VIDEO \
It is called i not j .... i , say it with me, i , they use i for (i)maginary notice that i in there? I know it is not imaginary but most people call it that and they named it after that so yeah use it as is
If you take something that is imaginary and try pin to something tangible is it still imaginary?
Andy P i said it is nothing but a name, call it by its name, that simple, no need for provocative examples😝
Electrical Engineers use j to represent imaginary numbers because they already use i for current
dudeitzryno thats dum.... in physics you use ( I ) for current, not ( i )
hasan kharfan hasan kharfan well in ee most people call it j so yea use it as is.
Thank you sir.
*E*