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 RUclips 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.
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
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.
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
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 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
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*.
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.
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
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
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.
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?
I dont understand why the college teachers cannot teach like this...they take way too much time, but only end up confusing the students. May be because they get paid too much...!!
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
![BLACK BAG - Official Trailer [HD] - Only in Theaters March 14](http://i.ytimg.com/vi/Du0Xp8WX_7I/mqdefault.jpg)
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 :)
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
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 😨😨😨😨😨😬😬😱😱
My teacher sucks so bad at teaching geometry im glad you do these videos to help people like me
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?
I love Khan academy!!!!! Thank you so much for helping me.
Thank you Sal. You are an inspiration. Through your help I have begun my RUclips 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
If only all people could teach like this with this sort of homework!
alexbat007 Some teacher do teach with videos.
great videos. College has no mercy for us math deficient distance learning students. These vids are a good resource for the lost.
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....
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 am the son of wounded Syria. We lost our homeland and we still want to learn ... Syria Damascus
It works if you fast forward few seconds.
Sal's voice is ASMR
New Bob Ross
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🕶️👓🕳️🕳️👢👒
namaste and thanks for enriching worlds knowledge through your endeavour
Legend
We thank for your nice activity of the RUclips
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.
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
Great explanation totally makes sense! I'm happy to know what I have coming this August !
These videos need to be rerecorded, its been 10 years Sal!
I appreciator your explanation skills
now why can't all teachers be this good?
Thank you for that good lesson. Much love!
nice videos. i have another different powerful explanation for complex numbers
You explained this so much better than my college professor ha
Nice work !! Wish i found dis earlier.
muy buena tu esplicacion, a pesar de que no hablo tu idioma, entendi, gracias!
CAPE Inte. Math on Monday... Thanks for the videos!
Very nice lesson
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
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?
So just as there is East, West, North and South,
In maths, there is
1,i,-1 & -i.
Hope this helps
Binnoy.
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! probably saved my grade.
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
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
Watching a productive 10 minute video instead of going to a 50 min lecture :D at home while eating subway :D
This video helped out a lot, thank you!
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 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
Thanks so much! I owe you tons!
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*.
Thank you so much. This was a lot of help.
Wow. You explain this way better than my teacher xD
you are a hero!!!
Thank you for this video! It helped me understand much better a hell lot! :)
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
Found this right after my test. Of course.
I also do complex numbers from past exam papers.
Complex numbers........... they sure got that name right
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....
thanks, really helpfull and with subs
what program does he use to explain this?
Find all complex numbers z satisfying z5 = 1 + 2j. How many complex
numbers satisfy this equation?
I'm so confused
This is all fine and dandy...but what does this have to do with Batman?
Looking up some hardstyle and I've reached exactly what I had to complete for my tutor.
Fate?
thank you so much i understand much better
would -3i also be a solution of (-9)^(1/2)? because if I square -3i I have -9
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
Is this for high lvls?
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
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.
1:40 I came to the exact point and asked: do the negative numbers really exist ???
Ty Sal. U sound like the guy from super Mario frustration
very helpful for review! thanks!
your the best :)
He said "image clear, image clear"
Angelica Joy Baloloy is the only one who has been ⛑️📿💄🦁🦁
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
No, root -9 would be 3i. -9= 9i^2, so root -9 is root 9 multiplied by root i^2, which is 3i
wouldnt root -9 be 9i? since root -1 is i??? im confused
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.
ahh thank you my friend for making that clear to me =)
Complex numbers!!
when he subtracted z1 - z2 why did he get (a-c) PLUS (b-id)i , emphasise on the plus linking the two there
Nooice.
Sweet thanks mate!
I dont understand why the college teachers cannot teach like this...they take way too much time, but only end up confusing the students. May be because they get paid too much...!!
wow you got some skills with the mouse...LOL
compute
z= cosa+sina+i(sina-cosa)
after findind
t*=a-pi/4
then what i will do and what will z+?
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?
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
what about linear vector spaces?
jirosei8 is greatly help you 😎🧘 👤👤 👤🗣️👤👤👤 👤🗣️ is greatly help me with this matter is greatly help you with
At which grade do u usually start learning this?
+timelordtori my school system is different then
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...
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
i heard that imaginary numbers were to be used in eletricity. respond to me if im right beacuse i dont really remember
@MilitaryMan006 It is 0.707 + 0.707i, or √(1/2) + √(1/2) i
@k0du123
It's used in electronics and fluid mechanics
why don't more teachers teach like this?
u may check his videos in other languages as well
GOOD
oh my god i love you!
Lol..
I just turned 14 a little over a month ago and I'm using this in Pre-Calc (Junior year).
wow ur so smart! how can i be like you??