Complex Numbers Part Imaginary, but Really Simple

In this BLOSSOMS lesson, Professor Gilbert Strang introduces complex numbers in his inimitably crystal clear style. The class can go from no exposure to complex numbers all the way to Euler’s famous formula and even the Mandelbrot set, all in one lesson that is likely to require two 50-minute class sessions. Complex numbers have the form x + iy with a "real part" x and an "imaginary part" y and that famous imaginary number i, where i is the unreal square root of -1. Professor Strang shows that we should not worry about i, just work with the rule i^2 = -1. Professor Strang can hardly control his excitement as he presents these results to the class. That enthusiasm is bound to transfer over to the students. The breaks between video segments challenge the students to work through examples, assuring that they have captured the essence of the previous discussion of complex numbers. The lesson sets the foundation for the students to move further in their understanding and working with complex numbers.

[@cyberlightbeing]

This man is such a brilliant teacher! I wish I had access to his teachings 40 years ago, thank you!

[@geethanjalibalaji5232]

haha

[@michaelnahole430]

I feel the same way prof Leonard you really simplify everything. you are gods gift to math students.

[@Anujkumar-rt6dc]

kzbin.info/door/nSzn6hUZk-M7juvSAK2Eqw Notes ke liye Anirudh Sir is the best.

[@robertw2930]

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>

[@IntelligentDiscussion]

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.

[@Alpffine]

nah he'll spank you if you can't do your math and you'll scream daddy.

[@ohyeahsubscribetomaximilia5694]

Lou king

[@georgesadler7830]

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.

[@nostalgia.haneen9421]

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 "

[@neurolife77]

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!

[@s9300097]

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.

[@madhushreebhagwat7877]

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

[@se2702]

What an amazing thing to be able to have a math lesson from this brilliant - world renowned professor. Absolutely wonderful man!!

[@SciHeartJourney]

Thank you Professor Strang! You really changed my life. I've had so much career success following your lectures online.

[@damnson1356]

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.

[@mathsmaths3127]

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

[@muhammmadkashif6784]

The GOAT 🐐 of professors.

[@Matchless_gift]

Sir you are God gifted teacher for us.we are lucky to have you as professor

[@j_adam9071]

Thanks very much professor your contribution to science and knowledge is 100% certified phenomenal. Thanks 🙏

[@RC-uo3ds]

This man is brilliant .... Huge respect for you Sir .....

[@tapologomabotho4366]

This is amazing!! I just love maths. Thanks prof. You're the best! I wish I had a prof like you back in college

[@jimjackson4256]

I gotta like this man and his knowledge.

[@MathLab4u]

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

[@VeraPastaEthiopia]

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!!

[@amramjose]

What a great lecture and professor!

[@hathuytu]

hahaha, an idea just raised in my mind owing to the lecture. Thank you so much.

[@Yashab360]

Love and respect from India

[@hedronsciences]

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.

[@ptyamin6976]

nice puns

[@joebrinson5040]

My favorite teacher

[@epakal]

Prof. Strang, awesome as always. Best!

[@clarkianperez6756]

i wish we had this professor in the philippines

[@SAJAN_ECE]

He is an amazing teacher!..

[@franrodri88]

You are incredible, thnak you for exist

[@bunny4173]

Gilbert strang is the man

[@alemayehufeyisa9008]

dear professor I Wish you to live long life, you are special man i like you so much thank you

[@2002budokan]

Gil has enchanted us again. Amazing lecture, thank you!

[@sarojpanday6236]

Thank you sir very much for providing outstanding intuitions

[@RedefiningtheConcepts]

A great Gilbert, awesome!👌

[@kaylynnl6210]

Amazing lecture! Math is just fascinating

[@asuka-ryo]

Man, I love this guy

[@hubertmargreiter3508]

I like all your uploads. I wish you would continue .....

[@tijanajovic8358]

Thank you sir! I enjoyed your lecture!

[@koyin1244]

It is really helpful for me . I drastically kind on learning with u

[@rintumondal131]

OK now I have no doubt about this awesome man! Such a great guy....

[@aryandey2429]

He is awesome

[@teddygraham7599]

Thank you professor, you have taught me so much.

[@hari8568]

I really loved the review in between so hilarious!!!!!

[@sakit4829]

Thank you master wugui

[@parthabanerjee1234]

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.

[@mhlengimthembu9351]

What a beautiful lecture.

[@aa697]

Great Great Stuff

[@mark_tilltill6664]

He is the Mr. Rogers of mathematics.

[@nahomgirma5501]

Really good lecture sir

[@boliu5809]

teaching so clearly, wonderful

[@ahmedchajia3478]

god bless you professor

[@robertclark2607]

I love the maths you explained so well :)

[@muhammadasyraf9490]

great lecturer! long live math

[@philmccavity]

he makes me want to buy chalk!

[@wellesleypublishers4939]

Gilbert Strang has released Indian editions of two of his popular mathematics books, in India. Details are at www.wellesleypublishers.com

[@pahadiGirlShobha]

u r amazing ur vedio is very helful for meee its gives a complete know ledge u r wonder ful🌼🌼🌼🌼🌼

[@peterpalumbo3644]

You are right. This is better.

[@ivornworrell]

*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.*

[@jake_runs_the_world]

Absolutely amazing !!

[@michaelcordova1803]

Excelent.

[@ummehabiba3681]

mittag-leffler expansion of sin (1/z)=? tell me the answer of this question

[@ecaterina_trofimova]

Thank you!!!!!!!!!!!!!!!!!!!!

[@ayhanamirah2183]

very very very..... good

[@mdtauseefibrahim323]

great sir.

[@SimonClc]

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]

In order to simplify it, 2/sqr2= sqr2×2/sqr2×sqr2= sqr2

[@eleniriga5513]

It's the same thing basically

[@SimonClc]

@@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

[@piousgold5207]

thank you sir for the lesson

[@takeyoubackward7524]

Great sir

[@mertcavusoglu6305]

ess dayıma efsanesin

[@selvams7061]

at 7.51 Y u divide by sqrt 2

[@SufiRepublic]

sadly u do not have playlists !

[@pendodigy]

Is it possible to find the answers to the exercises anywhere??

[@shreyassinha1207]

You can Google the solutions of x raised to 8 =1

[@devenderreddy9608]

Sir diagrams r pentastic

[@sountheara9307]

Hi Sr u has exercice about Complex , I come from Cambodia

[@justinfleagle]

What are the applications of complex and imaginary numbers?

[@HighestRank]

Licher salsa first obviously is to provide all n solutions to an ńth order algebraic equation with unknown variables.

[@robertw2930]

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

[@robertw2930]

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

[@sucikman]

why i times i gives you 1 not i squared???

[@jay-hk1wb]

thanks sir

[@zawhtunnaing3036]

which number is grater than, 2+3i and 2+5i ???

[@prospeaker323]

We can't know , in fact we can't compare complex numbers because the value of i is unkown

[@seleccionPersonal1]

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 )

[@afuadebra2498]

Where from the square root of two? Please help

[@Gabeee]

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

[@HighestRank]

At 8:50 it is the denominator in practice example #1 contrived simply for an exercise called ‘Activity 1’.

[@andresrequenatappi6771]

fantástico

[@ricchburglar]

wow x squared minus 5x plus 4 equals 0 huh. Things are getting real in here. GREAT CLASS BY THE WAY👍🏾👍🏾👍🏾

[@ДаниярАзимов-и8о]

Respect

[@adanwillams3684]

Nice

[@pocojoyo]

Actually, the solution to x^2 + 1 = 0 is +i or -i.

[@pocojoyo]

ok, he added the negative solution a minute later...

[@erwinmeza2826]

Strang well...

[@operazionetrasparenza5297]

T H A N K Y O U !!

[@seoexperimentations6933]

So what is Z^2?!? I got i

[@mustaphaelammari1128]

Z=a+ ib then Z^2= (a+ib)*(a+ib)=a^2 - b^2 + 2*abi

[@robertw2930]

:. i thought meant therefore in math

[@robertw2930]

no mAYBE DIDDFERENT IM THINK LOGIC NOT THE ...(ELIPSES?)

[@annehinrichs22]

They should name a country after z and z bar

[@ayonbiswas4186]

Zanzibar: Say no more!...

[@wildenthusiasm]

Iota

[@Chandinishetty2682]

So dark chalk

[@veneshahenry8853]

Give some more number

[@HighestRank]

venesha henry which, imaginary&complex or real?

[@google6730]

Not realy simple :(

[@ChechoColombia1]

at 7.51 Y u divide by sqrt 2

[@marciomarquesdarocha211]

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.

[@ChechoColombia1]

@@marciomarquesdarocha211 thank you, for real