This guy really knows how to teach,as in,how to get things inside the most clueless of the heads,I would wager these videos are better than most local tutors you would find in US,some would charge huge money for the iinfo contained in this tiny vid,so Mr.Khan,you have our most dear thanks :)
Thank you Sal. You are an inspiration. Through your help I have begun my UA-cam videos. It was a bit daunting at first but now I am getting into the swing of it. I have watched your style and your relaxed manner has helped enormously. I don't worry as much when I make a mistake and this makes it more enjoyable in the presentation. I believe that we are providing great opportunities for students wh cannot afford textbooks or are too far away from a school. Once again thank you. John Kinny-Lewis
Thank you so much. It makes me wonder why math books and math teachers make it seem so difficult. What I couldn't understand after 3 hours of studying from my mathbook, I now do understand in under 20 minutes watching your video.
I could save a shitload of money just staying home and watching these videos all day, I would definitely learn more. To bad I have to pay thousands of dollars for a piece of paper with my name on it....
Okay so I actually enjoy math to some extent, but this chapter ticks me off. And you just made it fun and easy to understand and it was funny. c: The dimension thing really helped haha. Thanks dude.
I had an interesting thought; if you graph the y axis vertically and the x axis horizontally, could you then use the “imaginary” axis perpendicular to that x,y plane and generate functions in all 3 dimensions?
I have a suggestion for you Khan. You should make a playlists that separate the curriculum from multiple subjects. One should have all of the Geometry Curriculum, Algebra 2 Curriculum. Pre-Calculus Curriculum, and etc. If you do that, I can skip two years in mathematics.
thank you so much for this. really easy to understand. i hope you were my calc teacher. i was wondering if you have any videos for sinusoidal steady state analysis
So a real number is magnitude, and the imaginary part of a complex number is also magnitude, but is orthogonal to the real magnitude? When you multiply by an imaginary part, you also rotate the vector 90 degrees pushing it into the other dimension? I'm not sure exactly how to say it, but am i understanding this correctly?
Gogargoat Yes. If you graph a quadratic equation it makes a parabola; however, the graph of the complex solutions to that same quadratic equation will form a parabola perpendicular to the Cartesian plane.
This is a great video, but be careful. i^2 = - 1 gives two possible definitions for i because i^2 = - 1 and (- i)^2 = - 1. The custom is to choose i = +\sqrt(- 1). There are really two models for the complex numbers. They are automorphic under conjugation z --> z*.
Wait. Is i bigger than -i? Is 2i bigger than i? Is there no concept of 'bigger' when it comes to these numbers? I suppose they're all 0+ni meaning they are all 0 with some other value that isn't really 0 but is on the real plane? But then you could say that all real numbers are 0i+n, making my point meaningless. Is it that they are bigger only on the imaginary axis and that real numbers get bigger on the real axis?
Complex numbers actually indicate rotation. i = rotation by 90 degrees. i^2 = rotation by 180 degrees = -1 = negative of that number. . i^3= rotation by 270 degrees = -i i^4 = rotation by 360 degrees =1. Rotation by 360 degrees brings the object back to the same position. Take any object in your hand and rotate it by 90 degrees 4 times. You will see that it comes back to as it was before rotation. There is a whole video dedicated to complex numbers on my channel, if you wish Binnoy
No, a complex number consists of a real and a imaginary part Bi can also be a complex nimber since the real number can = 0, so bi+0 is still a complex number and vice versa
Thanks for that... Mr Khan, could you please tell me what software / e-pen / digital pen you are using. I am looking for user-friendly delivery platform. Thanks in anticipation. Moctezuma
Complex plane was invented to measure rotation, just as a normal x-y plane is used to measure change in size, length, distance etc. Binnoy Visualizing Maths A book beyond Formulas
I don't get this thing. In book CN i defined as ordered pair (x,y) x and y real. Then it defines i as (0,1). It also defines Re(z)=x and Im(z)=y. Then addition and multiplication ....then book writes (x,0)=x plz explain this. I figure out this only Re(z=(x,0))=x But how (x,0)=x??. Soon my exams are from 23rd
This video is so nice but I am used to a so high level of quality now so the lack of pop filter annoys me so much but hey dont worry for me its still a great teacher and a nice video
For those discussing the quality, youtube videos actually slowly degrade in quality over the years and develop some artifacting, which has been proven on a number of occasions. This is most likely caused by the video files being moved from server to server, compressed, copied, or otherwise disturbed over the years since they were initially uploaded.
my maths teacher does this sometimes...problem is there are some really smart people in my class so she get's away with it alot of the time...I mean... I get it.. eventually after much difficulty, but It doesn't need to be so hard - _ -
This guy really knows how to teach,as in,how to get things inside the most clueless of the heads,I would wager these videos are better than most local tutors you would find in US,some would charge huge money for the iinfo contained in this tiny vid,so Mr.Khan,you have our most dear thanks :)
The most soothing voice on the web.
ikr
Well, second most soothing voice on the Web. There are video recordings of _The Joy of Painting_ by Bob Ross
Most scary voice 😨😨😨😨😨😬😬😱😱
Stop scrolling down, and focus on the video.
BENACHOUR Abdou ok sorry
My bad
yea my bad, thanks for looking out for me
1➗♻️💤🖼🎼❄️😢math classes in university establish myself as career ready.
Ok thanks for the warning lol
I wish Khan would re-do these videos in higher quality so they were easier to look at. Still great though!
Is it possible this is a dupe channel fishing for likes?
@@pebble2259 It's a video from 2008. What would you expect?
My teacher sucks so bad at teaching geometry im glad you do these videos to help people like me
Thank you Sal. You are an inspiration. Through your help I have begun my UA-cam videos.
It was a bit daunting at first but now I am getting into the swing of it. I have watched your style and your relaxed manner has helped enormously. I don't worry as much when I make a mistake and this makes it more enjoyable in the presentation. I believe that we are providing great opportunities for students wh cannot afford textbooks or are too far away from a school. Once again thank you. John Kinny-Lewis
great videos. College has no mercy for us math deficient distance learning students. These vids are a good resource for the lost.
I love Khan academy!!!!! Thank you so much for helping me.
If only all people could teach like this with this sort of homework!
alexbat007 Some teacher do teach with videos.
Thank you so much. It makes me wonder why math books and math teachers make it seem so difficult. What I couldn't understand after 3 hours of studying from my mathbook, I now do understand in under 20 minutes watching your video.
what my tutor coulndnt teach me in a week............sir,u taught me in 10 mins.............thnk u so mch sir......i will surely get gud mrks
I could save a shitload of money just staying home and watching these videos all day, I would definitely learn more. To bad I have to pay thousands of dollars for a piece of paper with my name on it....
love these kind of videos they explain and make things clear!
Victor Navarro is greatly help me out and have fun in Florida for the best for🕶️👓🕳️🕳️👢👒
Okay so I actually enjoy math to some extent, but this chapter ticks me off.
And you just made it fun and easy to understand and it was funny. c:
The dimension thing really helped haha. Thanks dude.
Thanks for the lesson! And for getting me to look up and learn the word monotenous! Such a sick word!
'I dont wanna confuse you' 1:52
No Sal, you're helping me with my degree
Sal's voice is ASMR
New Bob Ross
namaste and thanks for enriching worlds knowledge through your endeavour
We thank for your nice activity of the UA-cam
I am the son of wounded Syria. We lost our homeland and we still want to learn ... Syria Damascus
2:00. I get annoyed at this too. Imaginary is a terrible name. They're just as valid as any other number. They're just different.
Then call them anything you want idiot.
Great explanation totally makes sense! I'm happy to know what I have coming this August !
I had an interesting thought; if you graph the y axis vertically and the x axis horizontally, could you then use the “imaginary” axis perpendicular to that x,y plane and generate functions in all 3 dimensions?
I have a suggestion for you Khan. You should make a playlists that separate the curriculum from multiple subjects. One should have all of the Geometry Curriculum, Algebra 2 Curriculum. Pre-Calculus Curriculum, and etc. If you do that, I can skip two years in mathematics.
It works if you fast forward few seconds.
I appreciator your explanation skills
Thank you for that good lesson. Much love!
yo, Sal, u saved me in calculus II, u do
Calculus III as well? I'm saveeeeed again. U have no idea how happy i was to hear ur voice
This video helped out a lot, thank you!
So just as there is East, West, North and South,
In maths, there is
1,i,-1 & -i.
Hope this helps
Binnoy.
In 1:25 if we defined I as -1 and we squared it wouldn't it become 1?
Im pretty late but I^2 is defined as -1 not I
These videos need to be rerecorded, its been 10 years Sal!
Thank you for this video! It helped me understand much better a hell lot! :)
Legend
now why can't all teachers be this good?
thank you so much for this. really easy to understand. i hope you were my calc teacher. i was wondering if you have any videos for sinusoidal steady state analysis
muy buena tu esplicacion, a pesar de que no hablo tu idioma, entendi, gracias!
CAPE Inte. Math on Monday... Thanks for the videos!
Thank you so much. This was a lot of help.
So a real number is magnitude, and the imaginary part of a complex number is also magnitude, but is orthogonal to the real magnitude?
When you multiply by an imaginary part, you also rotate the vector 90 degrees pushing it into the other dimension?
I'm not sure exactly how to say it, but am i understanding this correctly?
Gogargoat Yes. If you graph a quadratic equation it makes a parabola; however, the graph of the complex solutions to that same quadratic equation will form a parabola perpendicular to the Cartesian plane.
This is a great video, but be careful. i^2 = - 1 gives two possible definitions for i because i^2 = - 1 and (- i)^2 = - 1. The custom is to choose i = +\sqrt(- 1). There are really two models for the complex numbers. They are automorphic under conjugation z --> z*.
Thanks so much! I owe you tons!
Wait. Is i bigger than -i? Is 2i bigger than i? Is there no concept of 'bigger' when it comes to these numbers? I suppose they're all 0+ni meaning they are all 0 with some other value that isn't really 0 but is on the real plane? But then you could say that all real numbers are 0i+n, making my point meaningless. Is it that they are bigger only on the imaginary axis and that real numbers get bigger on the real axis?
Consider the modulus of a complex number as its size:
mathworld.wolfram.com/ComplexModulus.html
thank you! probably saved my grade.
Complex numbers actually indicate rotation.
i = rotation by 90 degrees.
i^2 = rotation by 180 degrees = -1 = negative of that number.
.
i^3= rotation by 270 degrees = -i
i^4 = rotation by 360 degrees =1.
Rotation by 360 degrees brings the object back to the same position.
Take any object in your hand and rotate it by 90 degrees 4 times. You will see that it comes back to as it was before rotation.
There is a whole video dedicated to complex numbers on my channel, if you wish
Binnoy
So all complex numbers do is turn the number into negative or positive?
No, a complex number consists of a real and a imaginary part
Bi can also be a complex nimber since the real number can = 0, so bi+0 is still a complex number and vice versa
This is all fine and dandy...but what does this have to do with Batman?
Thanks for that... Mr Khan, could you please tell me what software / e-pen / digital pen you are using. I am looking for user-friendly delivery platform. Thanks in anticipation. Moctezuma
Very nice lesson
nice videos. i have another different powerful explanation for complex numbers
would -3i also be a solution of (-9)^(1/2)? because if I square -3i I have -9
You explained this so much better than my college professor ha
Nice work !! Wish i found dis earlier.
Find all complex numbers z satisfying z5 = 1 + 2j. How many complex
numbers satisfy this equation?
Wow. You explain this way better than my teacher xD
Complex plane was invented to measure rotation, just as a normal x-y plane is used to measure change in size, length, distance etc.
Binnoy
Visualizing Maths
A book beyond Formulas
I don't get this thing. In book CN i defined as ordered pair (x,y) x and y real. Then it defines i as (0,1). It also defines Re(z)=x and Im(z)=y. Then addition and multiplication ....then book writes (x,0)=x plz explain this. I figure out this only Re(z=(x,0))=x But how (x,0)=x??. Soon my exams are from 23rd
what program does he use to explain this?
why is this in the first half of algebra? i personally dont have a problem with that but i dont understand this kind of order...
This video is so nice but I am used to a so high level of quality now so the lack of pop filter annoys me so much but hey dont worry for me its still a great teacher and a nice video
compute
z= cosa+sina+i(sina-cosa)
after findind
t*=a-pi/4
then what i will do and what will z+?
Watching a productive 10 minute video instead of going to a 50 min lecture :D at home while eating subway :D
Is this for high lvls?
when he subtracted z1 - z2 why did he get (a-c) PLUS (b-id)i , emphasise on the plus linking the two there
you are a hero!!!
wouldnt root -9 be 9i? since root -1 is i??? im confused
At which grade do u usually start learning this?
+timelordtori my school system is different then
i heard that imaginary numbers were to be used in eletricity. respond to me if im right beacuse i dont really remember
just one question but you say i^2=-1 and i get it but then you say sqr(-9)=3i why not 3i^2
Because that would equal -9, not root( -9), as shown early in this video.
Edit: actually 3i^2 would be -3. (3i)^2 is -9
1:40 I came to the exact point and asked: do the negative numbers really exist ???
I also do complex numbers from past exam papers.
I am new to this. Why does i^2 = -1?
Ethan Segat because i = the square root of 1
So if you square both sides, i^2 = -1
It just is. It's like saying why are bananas yellow
@@Suggy08 because its evolutionarily good for them
Looking up some hardstyle and I've reached exactly what I had to complete for my tutor.
Fate?
thanks, really helpfull and with subs
For those discussing the quality, youtube videos actually slowly degrade in quality over the years and develop some artifacting, which has been proven on a number of occasions. This is most likely caused by the video files being moved from server to server, compressed, copied, or otherwise disturbed over the years since they were initially uploaded.
Interesting....
thank you so much i understand much better
what about linear vector spaces?
jirosei8 is greatly help you 😎🧘 👤👤 👤🗣️👤👤👤 👤🗣️ is greatly help me with this matter is greatly help you with
No, root -9 would be 3i. -9= 9i^2, so root -9 is root 9 multiplied by root i^2, which is 3i
@k0du123
It's used in electronics and fluid mechanics
Complex numbers........... they sure got that name right
your the best :)
Found this right after my test. Of course.
very helpful for review! thanks!
can you solve this one
α+iβ=1/a-ib complex number to prove (α^2+β^2)(a^2+b^2)=1
Nipun Rathi use the trigonometric formulas.
@MilitaryMan006 It is 0.707 + 0.707i, or √(1/2) + √(1/2) i
Skip to 4:18
I wish the writing was consistent. Some 2's looked like 7s, equal signs looked like C's and i's looked like L's.
Ty Sal. U sound like the guy from super Mario frustration
@caseywtw The imaginary number i is defined solely by the property that its square is −1
ahh thank you my friend for making that clear to me =)
I'm so confused
Why doesn't this work? I have to go to my calculus resit in an hour :P
when you see this comment from 3 years ago xPPPP
so how did you do the resit?
u may check his videos in other languages as well
I think there is something odd with his equation on subtraction
my maths teacher does this sometimes...problem is there are some really smart people in my class so she get's away with it alot of the time...I mean... I get it.. eventually after much difficulty, but It doesn't need to be so hard - _ -
Sweet thanks mate!
The video doesn't work :-(
wow you got some skills with the mouse...LOL
cAn someone plz tell meee wat iz: a + bi ?
@IAMMATSUDA have you never heard of short hand informal writing