Imaginary Numbers Explained Bob Ross Style

[@z3lop59]

At 9:27 shouldn't the blue cos have an offset of 90°? like this it's two sin waves but not one sin and one cos.

[@tibees]

I think you're right! Sorry for the mistake

[@ungabunga7574]

I don’t understand any of this but I still watch it

[@sm6756]

Yeah the blue graph should be 1 at x=0

[@z3lop59]

@@tibees Errors happen, I liked the video though.

[@kshitijsharma3170]

She's so wholesome

[@aromview]

The level of care put into these videos is matched only by Spongebob tucking pickles under a cheese blanket and reading them a bedtime story.

[@peterbrough2461]

We're not here to tuck pickles. (Margot made me say it)

[@rishabhjain3840]

*Analogy*

[@claytonmoore3869]

Tibees is the person we all need. She's so relaxing and calm

[@manbeardogstar]

I remember the first time I sat down to learn maths when a friend of mine recommended this channel. I've never looked back. I'm so grateful for Tibees. This has changed my life for good.

[@toz_dumann]

@@manbeardogstar why did you sat down for this?

[@manbeardogstar]

@@toz_dumann Because I want to make some imaginary friends :)

[@teja7976]

I got ASMR already

[@5Julius]

Agreed.

[@itsmemailingyou4234]

Tibees is an imaginary friend for many people, while being real.

[@BartKuipersdotcom]

If only she now responded to this comment by saying: It is I, that would be so wholesome ;)

[@binodtharu8348]

True

[@jillybe1873]

A paradox?

[@gyrgrls]

Imaginary lover doesn't turn you down.

[@govcorpwatch]

What matters is the magnitude, not the dimension.

[@mrbjjackson]

I was taught imaginary numbers in a 3 year engineering degree, and also have watched a load of KZbin videos including the whole of the "Imaginary numbers are real" series and this is the first time I feel like I've got a grasp of why imaginary numbers work and are useful. It was your line about "imaginary numbers are good at describing circular motion" that really made things click. Als the 45° example. Thanks very much 🙏

[@fizyknaut8108]

I remember finding out about imaginary numbers and being like "OK, cool... but why?" This explains it really well.

[@pedrocenturion7599]

I really started to go nuts with Imaginary Numbers. But, I mixed it with Kantian definition of Numbers. He negates the whole concepts negative numbers. Okay. But it sums what is just a negative sum for saying mathematics. It is just a Whole number with negative Numbers.

[@SuperSuperka]

The start must why is it a problem to have sqrt-1, I mean start from the rules of multiply and dividing positive and negative numbers. And then start to explain why we began think of new numbers bacause of that. Math has other non-sence expressions but mathimatians don't try to figure out new numbers each time

[@akse]

Yeah same.. didn't remember teacher really putting out a good examples why would we need them.

[@belkyhernandez8281]

Yup. They always got under my skin. I was like "Ok, they are just making stuff up to mess with us."

[@megarotom1590]

Cubic root solution formulas (even ones with real solutions) and trig (Holy cow imaginary numbers make trig 70% more bearable)

[@alpereng4652]

I m an high school student in Turkey. Our educational system is all about rote learning and the curriculum is too overloaded. This kind of videos ( logically explaining..) really helpful. Thanks a lot

[@youtubehandlesareridiculous]

That's also how it is here in America. :(

[@syednaseeruddin5689]

@@youtubehandlesareridiculous Wow really! So even America is no different to Turkey or India or whichever country that's facing rote learning and all.

[@deviladvocate21]

I live in the UK, and unfortunately it is the same here. The closest thing we get to an explanation is "because if you put it in a calculator, you will see it is the right answer every time", which is hardly an explanation at all.

[@kathanshah8305]

S(h)ame

[@kathanshah8305]

@@deviladvocate21 you guys are getting calculators we directly jump from doing it in mind / paper to holy wolfram

[@chrisphistry5949]

That really started to make sense! It's been over 30 years since I learned about imaginary numbers and only now are they starting to make any sense. More "Joy of Mathmatics", please and thank you.

[@maximillianwunderlich6179]

That one dislike is from tibees... the cat accidentally clicked on the mouse

[@beactivebehappy9894]

Did you just dislike a video to make a joke

[@vermillionreaper]

@@beactivebehappy9894 maybe you were the one who disliked it and you blame him so you get away with it, hmmmmmmmm...

[@JashXD]

There is 2 now, she made an alt account

[@lesselp]

Now 13 accidents

[@JashXD]

@@vermillionreaper sus

[@EayuProuxm]

4:43, why is Tibees in the back? Tibees: This is the negative real world This is one of the greatest pieces of cinematography I've ever seen. Style and content perfectly fuse to produce meaning! This youtube video needs to be archived for future generations.

[@bobhearinger]

This is gold! But is it real or imaginary?

[@randomnws]

Not only that, but after she finishes the "journey", as she turns to the side and displays the "map" of the plane on screen, and it lines up perfectly with where she and her drawing went along the journey. Honestly the video is art itself.

[@michaelhowell2311]

I don't know what to say about I've seen so much in the last five years I can almost believe anything is possible

[@watsoncrick6071]

ive studied imaginary numbers before but im pretty glad to say that I've gained a new perspective on this topic!! Thanks Toby!

[@zanop15]

That cat’s cuteness is immeasurable! It’s just like trying to use a ruler to mesure the sqrt(-1)

[@aniketeuler6443]

😂😂😂 that's a good one😆👍👏

[@levani7851]

immeasurable means irrational, sqrt(2) would be one. I know what you meant though :d

[@einsteinonblitz2345]

my (happiness) is inmeasurable and my day is (made)

[@zanop15]

@@levani7851 Yeah I went to far... but the sqrt(-1) still being immeasurable, it was more because of the context, but thanks for the correction anyway :D

[@lc1777]

@@levani7851 but aren't irrational numbers measurable? We can measure then on number line by Pythagorean theorem?

[@mohamedkhan5198]

If you were my Math's teacher, I would be PhD mathematics today.

[@hahahumble]

me too

[@rav1495]

muhammad tell me something about LGBT in your Muslim religion

[@bermu6]

@@rav1495 where did that come from? Hahaha

[@sam_9228]

@@rav1495 what

[@SureshKumar-md1hm]

I would receive Nobel if she taught me

[@FirefoxGuy18]

Your voice is very calm and soothing.It’s captivating and helps to make learning easy

[@lostandfound3588]

Watched this twice because of her voice, it's like she makes my brain feel my heart beat

[@BlackHermit]

Traveling back and forth between the real world and the imaginary world feels so wonderful! Thank you so much for providing us with these precious passports, Toby!

[@dianefeinstein8951]

I just love listening to your smooth soothing voice. I was sitting by the kitchen window looking out to my parent’s patio still holding my school bag and watching your program on my iPad. I woke up with my iPad on the floor and I had to rewatch you. I would love having you as a prof...it’ll make me actually want to attend classes. Love you so much, Toby. ...Diane.

[@VanCamelCat]

This is so enveloping and hugging. There is something just magical about the way you go about it all. I wish I had a teacher like you as a child. I would have excelled much further and would have felt supported instead of stressed by the mathematics & physics that I bonded with so well, whilst not bonding well at all with the humans that taught them to me - which in combination with a difficult household environment, led to me not advancing with math despite that huge potential teachers kept telling me I had. I think what I'm trying to say, is thank you, and I believe you are wonderfully magical and pure. Do you teach children? Have you considered it? Some of the more talented ones are talented because it's their escape, and they may need a guide through the door to imagination. Again, I wish I had you as a teacher growing up ♥ No one else understood my attempts at four dimensional humor, either. You totally would have.

[@MrU4theChillWind]

Your Bob Ross style videos are always a treat.

[@thegenxgamerguy6562]

I really enjoy the picture. I especially like that you included the roots of the trees in there, and in a way that they show that they draw the nutrients from the ground.

[@MB-ue2rf]

Never knew math could be so peaceful and relaxing, thank you

[@learnmoreushe3678]

I left the topics on imaginary numbers in my text book years back, untouched. Now they are courting me again. What a way to relax my mind, listening effortlessly to Tibees' genius teaching style. She's like Vivaldi piece, listening to her.

[@karora]

I remember learning about imaginary numbers at high school, and thinking "what a waste of time". And then a few years later I was training as an electronics technician (late '70s), and learning that I had to use imginary numbers for waveguide engineering calculations. Not so imaginary now, I thought!

[@karora]

@@WilliamHelstad On the other hand, having learned it once, re-leaning it the second time when I could tie it into the real world meant I learned it a lot faster and more throughly.

[@bonjourcoco]

Hello Tibees, (1+i) is not on the circle, so there's a sqrt(2) factor involved as well as a rotation. Our intuition can easily be carried away by (1+epsilon i) which is indeed a infinitesimal rotation :-) That said, very nice video as always. I love your work and your way of presenting things, which is always clever, beautiful and elegant. Thanks for being who you are and best regards.

[@agimasoschandir]

Isn't shown on the circle😕

[@robharwood3538]

Such a great video! Thanks! I've never read _Alice Through the Looking Glass_ but as you were drawing and placing yourself inside and outside the 'imaginary' world, and the 'negatives' of those worlds, I thought of that story and was thinking it could totally be an allegory about imaginary and negative numbers. I wonder if Lewis Carroll had that in mind?

[@arnavchoudhary7674]

I’ve been watching your videos from quite some time now. You’ve been fantastic in explaining each and every concept and your review videos of different examinations are also great to watch. Best of luck for your future endeavours!✨

[@TheK3vin]

these videos are just, truly magical

[@fernandodelgado6134]

Very nice to see you again! It's been a very visual explanation of complex numbers. I have never try to understood as rotation while we are multipling by i number. Now I have a more clear concept of a complex number. Thank you!

[@Darkev77]

This is really mind opening! Lovely presentation and in a fun way, honestly great job!

[@ZergD]

Favorite series from your channel dear Tibees! Thank you so much!

[@freddietickle732]

I can’t express how excited I am that this is back

[@deadbzeus]

One of the best maths series on KZbin. Running the concepts along the bottom helped it feel even more true to the original.

[@TheBoss-jc6le]

I love this series so much!! It's very relaxing

[@henrahmagix]

The change of camera angles made everything so clear!!!

[@sciencepetr5179]

YESSSSSS. Joy of mathematics is back!

[@topf_toepfer]

I was waiting for this so badly... This type of video is what makes this channel so unique, thank you toby!

[@kieronrobson7696]

You taught me more in 10 minutes than my Physics professor did in a semester

[@moonster2343]

I hope you're joking

[@irrelevant_noob]

why would you expect to learn about complex numbers from a Physics class? 😕

[@Mr.Blasss]

You need to pay more attention

[@James-hu6fz]

this is actually a phenomenal introduction to imaginary numbers i appreciate how simply explains this *complex* subject matter

[@danielpalmer643]

That was unbelievably good. I've filled notebooks on imaginary numbers and operations with complex numbers, but that was excellent.

[@RussellSubedi]

This is my new favorite quote regarding imaginary numbers: 6:42 "Despite the name, they are not imaginary at all. Some people just have trouble seeing them."

[@irrelevant_noob]

TBF, _all_ numbers are imaginary. 😏

[@wandadumas5810]

Saludos desde Puerto Rico. Me encanta la forma como has explicado este tema. Es fantástico como integras el arte y la narración con las matemáticas .

[@samsonrodrigues7942]

This has to be the most soothing voice ever recorded by a human❤️❤️❤️

[@nickvolkert3450]

Hooray! Absolutely fantastical and enlightening vid. Thanks.

[@_Longwinded]

What can be more adorable than this. I teach maths to small grade students in exact the same way ma’am does. but we gotta appreciate her drawing skills too! Thanks!

[@Zeddex2965]

Such a relaxing math lesson from such a wonderful teacher 😊

[@aidis138]

I just wanna say your videos always (well, not exactly always, but) helped me stay afloat since I discovered this channel back in somewhere 2018 (August or September, I guess). Thank you. What can be better than such form of escapism...

[@lucasbernard5304]

this is one of the best videos on the internet

[@MrCiroII]

Hi Tibee! Im your imaginary friend from Brazil. Im glad to watch your content, its creative and interesting. And of course, your kind way to teach science is absolutely lovely.

[@الصوتالرخيم]

So relaxing explanation your accent is southing too 😍

[@elba_magellan]

"But mostly we will be learning how to escape from reality..." . Glad you got down to business quick, lol. Why I love this channel.

[@billk9856]

Thanks Toby.

[@NicholasPellegrino]

Very relaxing and informative. I'm guessing most of your viewers already know about complex numbers, but this was enjoyable to watch!

[@ilovesustainableenergy9563]

interesting to think about what other numbers we don't yet know about... thanks for making maths so enjoyable Tibees :)

[@andrzejdubiel3263]

I learnt about imaginary numbers 16-17 years ago. I used them many times, I know how to calculate them. For all these years I didn't know about this angle rotation like from your example. This story about a forest and changing path by 45 degrees and how we can calculate this using imaginary numbers... IT'S BRILLIANT! Now I understand why I need it 😂

[@Dorddis]

This was so sweet! Just finished class on advanced complex geometry.

[@magicagrnub620]

What grade are you in

[@Dorddis]

@@magicagrnub620 preparing for entrance exam for engineering Bachelor. You can say i cleared grade 12.

[@magicagrnub620]

@@Dorddis Where you from bro, and ay ay that’s great.

[@Dorddis]

@@magicagrnub620 India bro

[@odiliomagalhaes5483]

I appreciate all Tibees explanations on any math subjects. Tibees has a very clear point of view; very precise reasoning; and a math problem solving technique that I call "UNIQUE AMAZING".

[@nolan412]

An imaginary friend needs an imaginary friend to say "oh yes. we're both real"?

[@mrghostlyr1162]

The calmess is intoxicating ! Makes me want to learn math on my own then following litearly the school circulum .. thanks teebs for making me a better person 😄

[@TheOmegaAlfa]

3am, I should get into another imaginary world but can't stop watching this video. :)

[@predatorb7647]

Honestly the best thing I’ve seen all day Thank you a lot, I used to love mathematics but since entering med school I haven’t had time to study it and this was vey nice to watch thanks again

[@stovegamesgames6917]

As soon as you revealed the map, everything you said came full circle

[@timothystockman7533]

"We're sorry. You have reached an imaginary number. Please hang up, rotate your phone 90 degrees, and dial again."

[@josephstalin7619]

My math teachers were never good at coloring or drawing stuff but yes they draw decent enough shapes for us to understand

[@anupamdebnath1884]

Your channel deserves way more subscribers.

[@aniketeuler6443]

Toby this manner is really nice like i just enjoy these kind of videos and don't forget your cat is damn cute 😄

[@Philomats]

We learn so much from you, much more than just mathematics: A way of being in the world. A pleasant way to teach. Art. Math. Kindness

[@luxemas1282]

Loving how she uses chalk as a medium.

[@davidargles]

I'm a 71 year old retired electronic engineer and I have to say that's the first time I've really understood why imaginary numbers are good for describing electromagnetic waves - thank you!

[@KalkuehlGaming]

As imaginary as my relationship with Tibee.

[@ThomasLahn]

This was a truly wonderful way to explain it. You are so *multi*-talented 😍 (I'm an astrophysics student, science tutor, and Bob Ross fan 🤓)

[@sushantrana9475]

Me after watching Tibees videos: I should top this year in Mathematics. But reality is often disappointing

[@salvatoreshiggerino6810]

I was told in first grade that you couldn't subtract a greater number from a smaller number. When I got home I was feeling a bit transgressive, so got hold of my father's calculator, and gave such a subtraction a try. When I reported back the results the teacher just said the calculator must have been mistaken. It was a pretty discouraging experience. In retrospect, I think I was searching for patterns so I could infer new knowledge from principles instead of spending time on tedious rote memorization, as I was very lazy as a child (and still is). It took 15 years for me to realise that this was the correct way all along, unfortunately being too lazy to do the rote memorization I ended up being quite bad at math.

[@michaelpr1]

Hi, I'm from Ecuador 😃🇪🇨

[@dermobbing-ratgeber5166]

You have such a soothing voice... if I ever should have sleep problems I will listen to your video.

[@aparecidoazariasazarias5450]

Thank's from Brazil...

[@inb4play167]

This was the saddest story I’ve heard all month. Not only did I have to go through the emotions as you worked things out between your negative friends and your imaginary friends, but I was also reminded of how stupid I am in real life.

[@αηομαλψ]

Thanks for making my day better

[@robertlozyniak3661]

Multiplying by 1+i does not just rotate by 45 degrees, it also stretches by a factor of sqrt(2).

[@vk2ig]

Indeed. The rotation required for maintaining the magnitude of the complex number is (1+i)/√2.

[@ephemeralnihilist]

Escaping from reality with Toby ❤️

[@user-ye3rq5cc9x]

Whoever has known mathematics deeply knows it's pure poetry. And with a voice you have is like you are reciting it. What a beautiful heart and curious brain you have ! 😊

[@loydv9506]

is this really how a genius mind functions? wish I had that thinking

[@brucekempf4648]

I just love how you explain math. I really wish I had a teacher like you when I was younger. You're the best!

[@GUDBROS]

good morning Toby

[@HTphyzycs]

I don't think I've ever quite grasped the concept of imaginary numbers until this video. Pretty amazing

[@mrraven9790]

Hi from Turkey 🇹🇷

[@keepthefaith9805]

turkey tail

[@jeffsiegwart]

You have a unique way of explaining complex math. It intrigues people to explore mathematics, which is a very intimidating topic for most. Thank you.

[@kauecampos8756]

08:08 I would get lost and die from starvation lol

[@randomalbum9879]

Lol even if I had the equation memorized or written down, I wouldn't know what any of it means

[@popnkids2.059]

I like your way of teaching and your calmness

[@emmanuelortegabeleno9503]

i^4 be like: snap back to reality

[@asdf12369]

KNEES WEAK

[@vk2ig]

Yep, it would make your head spin ... by 2π.

[@disekjoumoer]

God Toby, this was simply brilliant. Truly amazingly well done. I've never seen anyone describe complex numbers with such a childlike joy and simplicity.

[@eshan4487]

Biggest fan from India, ma'am 🙃

[@tombufford136]

Very helpful this Toby. Nice way of coping with Vectors in rotation used in AC electrical theory, generators and motors. i, j and k vectors in 3D force analysis. We are blessed with your beauty in this video Toby not usually found in Engineering Classrooms !

[@dotexe3301]

Thing make us to luv her more is She combine relaxation with mathematics😍😍😍🤩

[@windgassen]

Thanks!

[@edwardlivingston2606]

No matter what she want to explain , she always remain calm . 😎

[@bringer-of-change]

Your abstract metaphors and peaceful voice makes me happy and blows my mind in a very good way 😶

[@dakoderii4221]

Don't stop watching halfway or you'll be trapped in Imaginary Land.

[@edwarddobrowolski1055]

Thank you, one of, if not the best explanations I have seen. This is helping me understand Voltage and load calculations when playing with three phase power.

[@RichMitch]

Meow

[@headfime]

love the absolute values in the end. they really spread some positivity! :) (and bring you back to reality)