Square root of i, explained Bob Ross style

Solving sqrt(i) from the comfort of my garden on a 35°C Australian summer day
*wipes sweat from brow*
Want to see this problem solved using only algebra? Watch this bprp video: kzbin.info/www/bejne/kGWcmYulg5l-jck
💌 Subscribe to my channel to see more videos like this: kzbin.info
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👁 Website: tobyhendy.com/​
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🐦 Twitter: TobyHendy​

[@tibees]

Featuring Henry the cat and Timmy the toad. Since I'm showing all solutions in the complex plane I'm really finding z where z^2-i=0

[@sujithmalawisuriya8033]

I would like to see you some day.🙂

[@nightkin]

Henry

[@letoatreides4041]

@@sujithmalawisuriya8033 that's not how you do it. "Tyger Tyger, burning bright, In the forests of the night; What immortal hand or eye, Could frame thy fearful symmetry? "

[@dijin456]

Its 20 below here.1.5 meters of snow.do the math

[@letoatreides4041]

ahh tibees has prospects

[@bigburd875]

Tibees: *performs math that is utterly incomprehensible to me* Me: "ah yes of course"

[@DoctorDew]

😎😅

[@alexnelson7258]

Glad I'm not the only one!

[@TOM-yd8ub]

I remember seeing COSTheta+SInTheta. I asked where is that from. Was told it just is. This makes way more sense now.

[@milangorgevski3290]

2:54 and just beat the Euler out of it. XD

[@kenshinhimura8708]

Tan's mom sounds dirty...

[@eigenchris]

I need to start saying this when I work through math problems.

[@grondo7224]

i cried HAHAHAHA

[@ypey1]

Lol brilliant, so unexpected i almost choked

[@raghothamkulkarni1552]

@@eigenchris why are you not posting?

[@MathAdam]

1:12 "Real friends can be complex too." Too true!

[@ickimadrasi8965]

You are the most pleasant instructor ever

[@Anon-tr2lq]

@@ahmedalshalchi What's that supposed to mean?

[@partyY2Hard]

yes agreed

[@schrodingerbracat2927]

That means he wants to befriend her on FB, but the relationship is going to be complicated or complex.

[@gigabit6226]

@@schrodingerbracat2927 some would say… imaginary Get it, cause, imaginary numbers?

[@lyrimetacurl0]

If you've watched Spongebob, you know to draw a perfect circle, first you draw a detailed image of a head and then you rub out everything except the circle, then you have it :)

[@BettyAlexandriaPride]

That's hilarious.

[@awesometani8148]

Yes.

[@hansvandijk1487]

It’s like making an elephant out of a rock. Just get rid of every piece that doesn’t look like an elephant. Greetings from the Netherlands 🇳🇱.

[@OnnoDijkman]

@9:30 that last explanation was exactly what I was looking for!

[@jattstud]

Your calm and composure are your best assets for teaching complex topics. Keep at it, the world needs more teachers like you!!

[@anikazk]

"talent is just pursued interest, anything you practice you can do" thank you so much for these lines

[@WXUZT]

Wish I was taught my STEM courses by this type of instructor. So nicely explained. Thank You !

[@leo9272]

I don't even know why I'm watching all these math and physics videos on KZbin lately but there's something very satisfying about math and physics. I think the fact that it's so difficult for me to wrap my head around all these equations and formula's and I really want to understand it, is what is increasing my interest in it. Oh and your videos are just fun to watch. Keep it up!

[@theopot5798]

I do not understand a thing of what she says...drawing faces and letters, and she says that this is logic

[@soft8oiled]

Math ASMR

[@martinramirezjr7872]

EXACTLY

[@mathematicallrecreations2437]

I do math history. Check it out if that seems nice.

[@andrewohara8920]

go watch chycho, its already a thing

[@masteronepiece6559]

I think you guys are in the wrong channel.

[@JeffreyBue_imtxsmoke]

totally

[@Hassony523]

She looks like a 1890 Texan farmer girl with that hair style.. I love it!

[@biggtk]

As someone who has recently failed Trigonometry (due to medical reasons/class absences), I'm just proud that I understand everything that Tibees explained, including the graphical, quadratic, and trigonometric solutions. *phew*

[@atulsureshkumar5109]

Get well soon!

[@sleatersan]

I don't know your circumstances, but I hope things are smoother for you from here on out! As someone who's had to take their share of medical withdrawals, I know how frustrating it can be (especially when you know you could've done well in the class otherwise).

[@blackpenredpen]

Go Henry!!!

[@aurithrabarua4698]

what about Oreo???

[@shashwat4920]

Why u don't have a grey ✅

[@CandidDate]

I pi, do you pi?

[@jarjuicemachine]

omg blackpenredpen

[@juancarlosfontanafontana909]

First move?

[@KibaNoTsubasa]

I can't help but smile in response to that face on the board. Edit: "Just beat the Euler out of it;" I lost it after that.

[@peterpiper6]

That would mean that Tibees made complex analysis friendly! ;D

[@kaushikgupta9490]

2:54 "just beat the euler out of it" -Tibees 2019

[@cawfeedawg]

You are a genius.. this is the first time in my life that I found math relaxing!

[@timthompson468]

Great video. I always had a mental block when learning complex numbers, since I was told since 3rd grade that a negative times a negative or a positive times a positive was a positive number, then i was introduced at the outset as the square root of negative one. “That does not compute!” It was a while before I could see that complex numbers were just a mathematical tool that broadened the application of mathematics (at least that’s the way I rationalize it now). So far, I’ve never run into the square root if i, but, if I do, I’ll know how to handle it. Thank you very much for your efforts. You’re a great teacher.

[@tombufford136]

Very pleased to have you walking with me through this complexity !

[@lnofzero]

Lovely presentation! You gave well paced clear geometric and algebraic explanations. Thank you very much.

[@icecreamforever]

Love the way you scrub the chalkboard!

[@iceboxchamberlain1]

This channel just inspires me so much to keep studying :-)

[@masteronepiece6559]

Best comment so far.

[@user-pb4jg2dh4w]

True

[@Manan0701]

Wow I never thought I would ever be able to do complex number problems but you make them seem so simple. Thank you so much! ❤️❤️

[@MidnighterClub]

Great video. I really liked when you pointed out that the negative quadrant was also a rotation that repeated twice got you back to i. Nice!

[@jrwntctv8091]

I applied to join Friendly Trees Anonymous, but unfortunately my application was declined. They told me that I was barking up the wrong tree, and I had to go and find another branch to join. The root cause of their not accepting my application was my lack of foliage. Can you be-leave it? :)

[@claudreindl7275]

You would have been accepted if you brought a trunk full of money.

[@briankelly5828]

Take a bough!

[@gorillaau]

No, I wood not! How should you get aboard with the FTA? Try going through the lumber yard.

[@tarmotaipale5704]

*be-leaf?

[@scottbaker4534]

You should be a local TV news anchor. You're PUNishing me with your wit. I would have said "They felled my application."

[@celt2453]

I'm shit at maths but love this channel. Help

[@hereb4theend]

You just need to eat more potatoes

[@celt2453]

@@hereb4theend True

[@Mackhelangelo]

@@hereb4theend church

[@nootics]

I was garbage at maths at one point but ever since I've watched these enthusiastic math youtubers I got much better at it. Not quite the math genius but definitely a lot better. Took me a year of watching to get grasp

[@gatewaytofarts2771]

Ireland read a mind for numbers

[@kenshinhimura8708]

I simply love your bob ross style explanations. Please continue to do more. Your content is amazing

[@TheAnubite]

Hey I just discovered your channel and I really like the way you explain things and talk about your journey through academia. I feel I can relate to most of the things you’ve experienced because I walked away from a PhD program as well.

[@Nityavidyardhi]

Wow I love this series toby, and your cute stories... also on your decision to quit PhD, I completely support and wish you all the best in finding happiness in whatever you choose...

[@nujuat]

The fundamental theorem of algebra implies that every square root needs a friend. *cries*

[@SIGSEGV1337]

Omg Alex I never expected to see you here

[@ArjanvanVught]

A lovely *relaxed* video for the Sunday evening. Thank you Toby.

[@emesclarke3393]

Tibees you're awesome! I didn't understand much of that but you sure held my attention right to the end!

[@SergeantTopBins]

YES i love these Bob Ross style vids!!!

[@Atharv_Nigam]

When you put that modulus sign after wishing all of us an "absolutely" mathematical day.. I screamed badly in happiness (weird) ! 😬✌️ Wish you luck tibees 🤘❤️

[@ChristopherDrum]

I believe that's the absolute value notation, not modulus, hence the "absolutely" tie-in.

[@Atharv_Nigam]

@@ChristopherDrum hey Chris, do you know that the same notation is used for the absolute value and modulus function, there is "absolutely" no difference between them

[@ChristopherDrum]

@@Atharv_Nigam No, as a programmer I never knew that. They're given completely different notation ( abs() vs. %) and do completely different things in my job. That they would somehow magically be the same did not strike me.

[@Atharv_Nigam]

@@ChristopherDrum okay no issues I am actually studying mathematics and I have no knowledge about programming.

[@aleeexandre3707]

Actually, I think you are both right, but referring to different things... Being French, I don't really know the exact English term, but modulus (% in programming) is indeed different from the absolute value, in maths it is used in arithmetics and to mesure angles on the unit circle ( 0 and 2*pi are equal MODULO 2pi) BUT the modulus of a complex number is its distance from the origin, and noted |z| as the absolute value. I don't know if there are 2 differents words in English, but there are 2 different notations for 2 different concepts. Hope I helped clear that out !

[@kamaldeepsingh2813]

I like how you keep smiling with every word you say #soothing. And henry seems like a good boy 🐈

[@chorthithian]

Rofl, your sense of humor is majestic. Made me chuckle so much. Gotta mention you have the aesthetic of an 18th century mathematician, which is awesome.

[@wolframalpha8634]

Hey I just wanted to say this : All the very best for your next journey and yeah even if I were to take a PhD I would end up dropping coz there would be a lot of holes , jump discontinuities and asymptotes on my PhD journey!! And plzz continue making such videos!!

[@peterpiper6]

Perhaps some of the discontinuities would be removable ;D

[@wolframalpha8634]

@@peterpiper6 might be if am systematic XD

[@jrwntctv8091]

Great video, you always have a unique way of explaining things which is a fantastic skill to have. I wonder if you could do a maths video in the style of a TV weather forecast?

[@Adenosene]

This video is so calming. I have never been so calm with mathematics before. Thank you @Tibees!

[@ixglocTV]

No thanks I've slept enough in maths.

[@maurofilho1259]

You explain smiling, clearly with joy, there is no price to someone like do the things like you do, congratulations from Brazil. Mauro Filho

[@danielfromca]

Great video - This is used a lot for AC current phasors in EE

[@vk2ig]

Only in EE we say √(-1) = j (because we use "i" for current).

[@MatthewBishop64]

"Beat the Euler out of it" hahaha. Nice one. :)

[@PsychedelicSlayer88]

I am absolutely in love with your voice, and your kitty, and your toad!

[@lilydapug5399]

This was actually so insightful. Just finished my precalculus course and I recognized some of the stuff we did! Even though I passed the class, I’ll admit I never totally understood the complex number lessons, this was helpful 😊 thanks! 🤗

[@Lord_Volkner]

I never have any idea what she's talking about, but I keep watching her vids.

[@marmikthakore7480]

Ma'am, I admire you for your knowledge, simplicity (and perhaps beauty.)

[@metal87power]

Perhaps??

[@mdmizanoorrahman2144]

All the time i see you is taking about studies. Your voice is so gentle. And you are so gentle. Your talking style is so innocent..... This really amaze me.... 🙂

[@HarshKumar-gc9zd]

Please keep it up! I love your channel so much... Believe me i have seen some guys and girls doing stupid things on KZbin just to get attention and revenue but you are doing thing that actually helps, thank you and keep up you work! May god bless you

[@ScottMorgan88]

While it's true that there are two roots to z^2 - i = 0, sqrt(i) is a function and returns just a single complex number.

[@Andrew-rl3uo]

True but it could be either of the two depending on which domain you choose for f(x)=x^2 in order find its inverse.

[@mike4ty4]

Yes. Or more accurately, sqrt(z) has a conventionally-defined "principal branch" which is taken to be that obtained by first analytically extending from the conventional positive square root on the reals to a cut plane cut along the negative real axis, and then extension to that axis itself is obtained by requiring it be continuous from above and discontinuous from below. Likewise, the same goes for log(z), and also the complex power, z^w - for all these, the choice of cut plane has to be the same in order for them to be consistent with each other. However, some authors may use a different convention to define this principal branch, since one can effectively arbitrarily create a branch in any way one likes. Thus, there exists the possibility for confusion, and so it may be more "natural" to treat sqrt, log, and complex power as "multivalued functions" (or better, one-to-many relations) in which all answers are fair game, so there is no arbitration as to what cuts or values one must use in that case. Tibees seems to prefer this latter approach, at least in this video. I would too; however I also recognize the utility of a conventionally defined principal branch, especially for computer software where that one must have sqrt(), etc. always return _some_ value and the usual behavior is to do as given above.

[@ayashroy2502]

It is imaginary no.

[@alexhoppe]

we stan

[@hansisbrucker813]

This was really enlightening. Thank you for your time.

[@davedave6650]

It really helps when a teacher is pleasant, calm, and doesn't rush through explanations.

[@dknicely1]

Why didn't my prof use a smiley face back in the 70's. I think I would have liked university math.

[@Voartist]

I would've liked algebra if she had been my teacher.

[@scottbaker4534]

Are you talking about the smiley chalk symbol, or the smiley prof?

[@jaimeduncan6167]

Beautiful video. May I ask if that is Schrödinger’s cat ?

[@brainboxanky1729]

No one knows weather the schrödinger cat 🐈 is alive or dead

[@jestemtomkiem]

Yes, it's not

[@danilomarvel5657]

no, IT IS

[@brainboxanky1729]

@@danilomarvel5657 explain further

[@danilomarvel5657]

@@brainboxanky1729 the cat is both dead and alive at the same time lol

[@conradpowers7953]

Loved the cat, the toad and music at the end. It is a nice touch :)

[@pranjal86able]

You are amazing! I love your videos. If this was actually hard to understand, I don't think it would be very enjoyable but this was easy to listen to and easy to understand. Watching at 12:00 AM from Newfoundland, Canada!

[@imaysin97]

a dash of aquamarine.

[@advaitpai1615]

i see cat i like

[@dayron9802]

I'm a simple man. I see Toby, I like.

[@dayron9802]

@@ahmedalshalchi, I saw Toby, I lost my head.

[@freddan6fly]

My gut feeling was right. Great work Tibeee. Was hoping for some chalk on the eye brows.

[@msiprime]

Omg thats what i learned today morning.... Watching YOU explaining it again will be awsm 💕

[@amayikdeb7569]

Joy of mathematics😂😂 It gives me pain😂

[@Engineer9736]

Pain can also be a joy

[@mathprof7776]

😂😂

[@keescanalfp5143]

@@Engineer9736, Pain of mathematics is scarcely curable. As your username already expresses. The joy of mathematics is hardly to be tamed.

[@scottbaker4534]

@@Engineer9736 Oh my...

[@RalphDratman]

Wonderful! Say, what is the connection between "Tibees" and "Toby" (or "Tobi"?)

[@tibees]

tibees is just my nickname :)

[@meispi9457]

@@tibees so your nickname is bigger than your real name👌

[@vivekmathur3514]

Coz wynaut

[@perrybrown4985]

Well, i'm guessing it is from aussies mocking your kiwi accent :-)

[@keescanalfp5143]

@@meispi9457, Why not.

[@briannalee6071]

I LOVE THESE VIDEOS TOBY💞

[@davidmaths]

Incredible: fast, simple and elegant to get the answer!

[@brad727]

What did 'i' say to 'pi'? - "get rational". What did pi say to i? - "Get real".

[@aldineisampaio]

And what did 'e' say to both? - Join me and we will be -one.

[@geepeeone]

@@aldineisampaio OMG, LOL!

[@123Iamawesome321]

But then 'pi' realized that 'i' was being a hypocrite.

[@Lakshin01]

0 dislikes ❤

[@boomboombasto]

your explanations are irresistible!

[@ksiordior1133]

i always fall asleep during your videos because your voice is to relaxing

[@WojtekBacza]

"Beat the Euler out of it" 😂. It got me thinking though, what if we replace "Euler" with "Devil"... - Devil's Identity - Devil's Number - Devil's Theorem - Devil's Method - Devil's Characteristic - Devil's Laws - Devil's Product Euler was Devil confirmed

[@francescosorce5189]

the original Zahlenteufel XD

[@scottbaker4534]

I think you may have tuned in to her complex and friendly humor.

[@utterlyhonest]

Science is pure poesy.

[@danielmago4327]

no it's not. In science we try to explain people things that are complex by words they understand; poesy is exactly the opposite (Sorry but english is my second lenguage)

[@utterlyhonest]

Daniel Mago Yes. But is science and poesy contradicting? Can’t a scientific explanation for a very complex problem appear to some people as elegant and poetic? Science and poesy are two separated objects, of course! But perceiving science as something poetic, some elegant way to explain our surroundings and it’s properties, is, in my opinion, very possible.

[@nantzstein3311]

@@utterlyhonest Poetry is different from one culture to another, not all humans make and understand poetry the same !

[@utterlyhonest]

Nantz Stein thank you for the clarification! Absolutely correct. Every human being perceives poetry differently.

[@nantzstein3311]

​@@utterlyhonest It all comes down to dopamine* stimulation* aka the pleasure of achieving something, be that figuring out the pieces of a poem line or an answer to some problem. That's what I believe

[@tombufford8659]

Very pleasant video, toby. After having struggled with imaginary relationships many years ago, a relief to be able to enjoy this with your efforts!

[@aaronramsden1657]

How freaking soothing is your voice!! Amazing!

[@mukeshchand5301]

This cat is so cute like You, Have an absolutely mathematical day.

[@kwadransdopolnocy]

7:24 :))))))))))))))))))))

[@CHEUKYINY]

OMG you have the superpower of making advanced maths understandable!! I enjoyed watching this so much, thank you for making this video!!

[@jamieg2427]

I loled several times. This was lovely. And honestly, I've always liked my radicals left in the denominator . . .

[@TheNachoesuncapo]

that starting music makes me feel like im in a romantic dinner...

[@TheNachoesuncapo]

@Yo Ming definitely imaginary

[@elwoodblues452]

I'd rather eat pie. Much less complex and fullfilling. I ask you beautifull young lady, how can such knowledge be of any practical use? Well explained though. Very well indeed. We need more tutors like you or shall we say "Bob Ross Style". To me ( with your magical voice) it's allmost ASMR. Yes, it tickles the grey cells! New Zealand?

[@vk2ig]

Nice tropical-looking garden!

[@jonathandavis7019]

I still love these art videos! You draw some excellent circles btw.

[@nantzstein3311]

I think my level is Basic Beginner in Maths, any advice Tibees ?? Med school ruined my Mathematics archive

[@johnchristian5027]

dont you just hate med school xd

[@nantzstein3311]

@@johnchristian5027 it's a toxic relationship. I think that med school hates me ^_^'

[@123arskas]

All that innocence + cuteness + voice just keeps me distracted. DAMN you're gorgeous......now time to learn about sqrt of i.

[@Edmondfreak]

Lol, thanks for writing that for me

[@123arskas]

@@Edmondfreak you're the sqrt of i?

[@nfineon]

hey I think I'm in love with your channel, really enjoy the outdoor settings and the replacement symbols :) But I'll be totally honest, I was really here just to see Henry the cat and learned somethings along the way niiiice

[@otonanoC]

My approval is immeasurable and my day is made.

[@dako2117]

who else googled friendly trees

[@HallBr3gg]

what I like the most about this channel is that "I'm about to break into laughter" smile.

[@erg0sum17]

Talent is just a pursued interest. Wow! this is so powerful.

[@avaevathornton9851]

That garden looks gorgeous.

[@klong1972]

I like how you are always smiling.

[@HarmlessOSRS]

Seeing you everyday gives me such a good feeling

[@timeless_realm]

I really enjoy your style of teaching.

[@ginismoja2459]

These videos are so relaxing and beautiful

[@neurotransmissions]

This was so cute! Your cat is great too

[@destyntobe]

Finally, you’re teaching me something i was studying recently.

[@jaketunes10]

This is adorable keep up the great work!!

[@gaintrain99]

Tibees for President 2020 - I cannot express enough how much of a boss you are, help me so much with math work

[@scootergreen3]

I like your cat. I've always heard people who like cats are nice people. You are very intelligent and way above my head.

[@ajjohnson9766]

I love these! Very relaxing and interesting

[@Eihell]

Personally speaking I enjoy this series please keep it up 🖤

[@MathsWithMelv]

Loving these videos!