I had to pause the video because I was so distracted at how much respect and love I have for this professor. Odd how you can tell when someone is a great human being, I know he'd never judge me for who I am, possibly except for my math skills, and even then he'd probably merely try to help me.
indeed the best math teacher i never knew ,but youtube mit open courses is great too bad I didn;t learn thi when I was 17-22 e to the i^2 isn't that almost euhler formula>
thank you I really feel happy with your lessons teacher I am a Muslim girl and in my country if we loved some one we pray for him by saying " may god give you more healthy life full of happiness without sadness "
Professor Strang, thank you for another beautiful lecture on complex numbers, Euler's famous formulas and the Mandelbrot set. In science and engineering ,Euler's famous formula is king.
This lecturer wrote many books I used throughout my study of mathematics. Wish he tutored me at the universities I attended. Great teacher and a huge thank you.
I was watching Prof Strang's lectures on Linear Algebra from MIT opencourseware and was puzzled with the reference to imaginary numbers. I don't have any background on them, so I decided to pause on it and try to get info about that. Imagine how happy I was to find this video sitting first on a youtube search for: "complex numbers mit opencourseware" ! I love math, but this guy makes it awsome! Great teacher, thank you!
i think we have lot of videos in youtube also from India not only about this concept but also for many other concept. but difference is that in our country we focus more on showoff which only helps for the companies to grow and not the students, students need these type of classes and lecture which have less showoff and provide a wonderful platform to learn the required concept more than a platform to waste their data. thank you sir for your wonderful lecture
You are humble ,down to earth and a teacher of superb understanding . Thank you so much Sir for teaching us in such a wonderful way. Thankyou so much Sir
best teacher i could have ever had . much respect. wish you all the best and only health and blessings may come your way. Only happy times. Stay safe professor.
Wow, great lecture. My objective is to translate equations to real life situations. This way e^z can be translated as the value by which a given image can be reflected such that the mutual viewpoint is the origin (zero). This means that if I projects something, then it will give a reflection and to value them equal (= understanding) I have to take an equal distance to both (projection and reflection) and that means I am back to myself at and as the origin of the whole operation. Whatever I project it tells something about me, the zero at/of/as the origin. "X" is in the I (=Eye) of the beholder.
Real nice & to the point introduction to imaginary numbers, i wish you would say something as to why people started to bother about complex numbers, what are their applications ?? Love you Sir, Thank you!!
Gill, I love the way you teach mathematics. It is so beautiful. I liked Mathematics but you have made me fall in love with it. You are a wonderful person.
*Nice video professor, but I must disagree with you @ **05:00** that Gauss is the greatest mathematician of all times:Have you considered The great Sir Doctor Albert Einstein, professor, and what of The Theorems of Pappus, The great Greek scholars such as Heron of Alexandria & Pythagoras etc.?Respectfully, learned professor.*
The concepts "greater than", "lower than" only exist if the kind of number are ordered. Complex numbers have not order. You can argue that distance to origin ( in polar representation ), could induce a concept of order, but this idea is not correct: 1.- all point in any circle centered in (0,0) are the same 2.- In fact you were using module of the vector ( actually R+ numbers )
I don't understand, when the addition Z + Zbar is performed, we get Z + Zbar = 2.(1/sqr(2)) = sqr(2). Why is that equality true? I don't understand why it's not just (2/sqr(2)).
@@eleniriga5513 yes, sqr(2)xsqr(2) is two, I guess when you put it like that it's fairly obvious! Thanks for your answer, it's interesting to practice this sort of basic flexibility in the way I perceive numbers
The ~distance of the complex number is sqrt(a^2+b^2) Z = a+bi, thus normalizing the 1+i complex number results in a distance of sqrt(2) and we normalize a vector by dividing its' components by the length, now altough complex numbers are not vectors, but they work the same way in this case, resulting 1/sqrt(2) * (1+i), if you take the length of that (by a^2+b^2 = Z(Z bar) ) it's 1
Observe z is a vector that measure 1 unity and 45 degrees respect real axes. Therefore, Re(z) = 1cos45° = 1/sqrt(2), and Im (z) = 1sin45° = 1/sqrt(2). Sorry my bad english.
I had to pause the video because I was so distracted at how much respect and love I have for this professor. Odd how you can tell when someone is a great human being, I know he'd never judge me for who I am, possibly except for my math skills, and even then he'd probably merely try to help me.
nah he'll spank you if you can't do your math and you'll scream daddy.
Lou king
This man is such a brilliant teacher! I wish I had access to his teachings 40 years ago, thank you!
haha
I feel the same way prof Leonard you really simplify everything. you are gods gift to math students.
ruclips.net/channel/UCnSzn6hUZk-M7juvSAK2Eqw
Notes ke liye Anirudh Sir is the best.
indeed the best math teacher i never knew ,but youtube mit open courses is great too bad I didn;t learn thi when I was 17-22 e to the i^2 isn't that almost euhler formula>
thank you I really feel happy with your lessons teacher I am a Muslim girl and in my country if we loved some one we pray for him by saying " may god give you more healthy life full of happiness without sadness "
Professor Strang, thank you for another beautiful lecture on complex numbers, Euler's famous formulas and the Mandelbrot set. In science and engineering ,Euler's famous formula is king.
This lecturer wrote many books I used throughout my study of mathematics. Wish he tutored me at the universities I attended. Great teacher and a huge thank you.
I was watching Prof Strang's lectures on Linear Algebra from MIT opencourseware and was puzzled with the reference to imaginary numbers. I don't have any background on them, so I decided to pause on it and try to get info about that. Imagine how happy I was to find this video sitting first on a youtube search for: "complex numbers mit opencourseware" ! I love math, but this guy makes it awsome! Great teacher, thank you!
Thank you Professor Strang! You really changed my life. I've had so much career success following your lectures online.
i think we have lot of videos in youtube also from India not only about this concept but also for many other concept. but difference is that in our country we focus more on showoff which only helps for the companies to grow and not the students, students need these type of classes and lecture which have less showoff and provide a wonderful platform to learn the required concept more than a platform to waste their data.
thank you sir for your wonderful lecture
You are humble ,down to earth and a teacher of superb understanding . Thank you so much Sir for teaching us in such a wonderful way. Thankyou so much Sir
What an amazing thing to be able to have a math lesson from this brilliant - world renowned professor. Absolutely wonderful man!!
best teacher i could have ever had . much respect. wish you all the best and only health and blessings may come your way. Only happy times. Stay safe professor.
The GOAT 🐐 of professors.
Thanks very much professor your contribution to science and knowledge is 100% certified phenomenal. Thanks 🙏
Sir you are God gifted teacher for us.we are lucky to have you as professor
This man is brilliant ....
Huge respect for you Sir .....
I gotta like this man and his knowledge.
Love and respect from India
This is amazing!! I just love maths. Thanks prof. You're the best! I wish I had a prof like you back in college
What a great lecture and professor!
Wow, great lecture. My objective is to translate equations to real life situations.
This way e^z can be translated as the value by which a given image can be reflected such that the mutual viewpoint is the origin (zero).
This means that if I projects something, then it will give a reflection and to value them equal (= understanding) I have to take an equal distance to both (projection and reflection) and that means I am back to myself at and as the origin of the whole operation.
Whatever I project it tells something about me, the zero at/of/as the origin.
"X" is in the I (=Eye) of the beholder.
nice puns
I of course subscribed and admire you. You r an idol. I am a math teacher. You remind me my professor when I was in university
Real nice & to the point introduction to imaginary numbers, i wish you would say something as to why people started to bother about complex numbers, what are their applications ?? Love you Sir, Thank you!!
My favorite teacher
He is an amazing teacher!..
hahaha, an idea just raised in my mind owing to the lecture. Thank you so much.
Prof. Strang, awesome as always. Best!
Gilbert strang is the man
i wish we had this professor in the philippines
Amazing lecture! Math is just fascinating
Thank you sir! I enjoyed your lecture!
Man, I love this guy
You are incredible, thnak you for exist
Thank you sir very much for providing outstanding intuitions
Thank you professor, you have taught me so much.
dear professor
I Wish you to live long life, you are special man
i like you so much
thank you
He is the Mr. Rogers of mathematics.
Gil has enchanted us again. Amazing lecture, thank you!
I like all your uploads. I wish you would continue .....
Thank you master wugui
It is really helpful for me . I drastically kind on learning with u
He is awesome
A great Gilbert, awesome!👌
teaching so clearly, wonderful
What a beautiful lecture.
god bless you professor
OK now I have no doubt about this awesome man!
Such a great guy....
You are right. This is better.
Gill, I love the way you teach mathematics. It is so beautiful. I liked Mathematics but you have made me fall in love with it. You are a wonderful person.
Is it possible to find the answers to the exercises anywhere??
You can Google the solutions of x raised to 8 =1
he makes me want to buy chalk!
Great Great Stuff
I really loved the review in between so hilarious!!!!!
Excelent.
great lecturer! long live math
I love the maths you explained so well :)
Thank you!!!!!!!!!!!!!!!!!!!!
Gilbert Strang has released Indian editions of two of his popular mathematics books, in India.
Details are at www.wellesleypublishers.com
Really good lecture sir
Absolutely amazing !!
sadly u do not have playlists !
thank you sir for the lesson
u r amazing
ur vedio is very helful for meee
its gives a complete know ledge
u r wonder ful🌼🌼🌼🌼🌼
very very very..... good
great sir.
Respect
What are the applications of complex and imaginary numbers?
Licher salsa first obviously is to provide all n solutions to an ńth order algebraic equation with unknown variables.
Great sir
fantástico
at 7.51 Y u divide by sqrt 2
Hi Sr u has exercice about Complex , I come from Cambodia
ess dayıma efsanesin
Sir diagrams r pentastic
thanks sir
*Nice video professor, but I must disagree with you @ **05:00** that Gauss is the greatest mathematician of all times:Have you considered The great Sir Doctor Albert Einstein, professor, and what of The Theorems of Pappus, The great Greek scholars such as Heron of Alexandria & Pythagoras etc.?Respectfully, learned professor.*
which number is grater than, 2+3i and 2+5i ???
We can't know , in fact we can't compare complex numbers because the value of i is unkown
The concepts "greater than", "lower than" only exist if the kind of number are ordered. Complex numbers have not order. You can argue that distance to origin ( in polar representation ), could induce a concept of order, but this idea is not correct: 1.- all point in any circle centered in (0,0) are the same 2.- In fact you were using module of the vector ( actually R+ numbers )
I don't understand, when the addition Z + Zbar is performed, we get Z + Zbar = 2.(1/sqr(2)) = sqr(2). Why is that equality true? I don't understand why it's not just (2/sqr(2)).
In order to simplify it, 2/sqr2= sqr2×2/sqr2×sqr2= sqr2
It's the same thing basically
@@eleniriga5513 yes, sqr(2)xsqr(2) is two, I guess when you put it like that it's fairly obvious! Thanks for your answer, it's interesting to practice this sort of basic flexibility in the way I perceive numbers
Nice
i is my favourite number ,but it hard i don't pretend to know trig much though i used to know where i was on the unit circle
Where from the square root of two? Please help
The ~distance of the complex number is sqrt(a^2+b^2) Z = a+bi, thus normalizing the 1+i complex number results in a distance of sqrt(2) and we normalize a vector by dividing its' components by the length, now altough complex numbers are not vectors, but they work the same way in this case, resulting 1/sqrt(2) * (1+i), if you take the length of that (by a^2+b^2 = Z(Z bar) ) it's 1
At 8:50 it is the denominator in practice example #1 contrived simply for an exercise called ‘Activity 1’.
why i times i gives you 1 not i squared???
Actually, the solution to x^2 + 1 = 0 is +i or -i.
ok, he added the negative solution a minute later...
Strang well...
mittag-leffler expansion of sin (1/z)=?
tell me the answer of this question
my head hurts now derrivates i know 1st and 2nd once get to third i'm lost e tto the ix^2 ? this is way above my paygrade
T H A N K Y O U !!
wow x squared minus 5x plus 4 equals 0 huh. Things are getting real in here.
GREAT CLASS BY THE WAY👍🏾👍🏾👍🏾
They should name a country after z and z bar
Zanzibar: Say no more!...
Iota
So what is Z^2?!? I got i
Z=a+ ib then Z^2= (a+ib)*(a+ib)=a^2 - b^2 + 2*abi
:. i thought meant therefore in math
no mAYBE DIDDFERENT IM THINK LOGIC NOT THE ...(ELIPSES?)
So dark chalk
Give some more number
venesha henry which, imaginary&complex or real?
Not realy simple :(
at 7.51 Y u divide by sqrt 2
Observe z is a vector that measure 1 unity and 45 degrees respect real axes.
Therefore, Re(z) = 1cos45° = 1/sqrt(2), and Im (z) = 1sin45° = 1/sqrt(2).
Sorry my bad english.
@@marciomarquesdarocha211 thank you, for real