Week1Lecture1: History of complex numbers

[@dimitriss1634]

This is hands down the best playlist about complex analysis on KZbin! Thank you very much Petra Bondert-Taylor! (you must have some connection with the famous Taylor!)

[@davidjones5319]

Thank you so much for posting this series. Phenomenal. Love the combination of the inception history with detailed techniques

[@bethwelodero1096]

The best lecture I have found on youtube, thank you.

[@oldcar8592]

I was looking at You tube videos on primes and somehow ended up here. Glad I did. This is a wonderful site. This instructor knows how to teach and goes into detail. Just as I got stuck at 13:40 with Bombelli's Idea equation, she did the calculation in detail. The professor seems to know just what the student needs to understand and then explains it. Years ago in college when studying circuit analysis, I was exposed to complex numbers, but their use in circuit analysis seemed to be just an afterthought and the concept somewhat hazy. Now that I'm a retired EE, I can really enjoy this lecture. She has a total of 36 lectures nicely broken up in reasonable sections. Don't know if I'm game for all 36, but I'm off to the second one now.

[@artsmith1347]

Yes! The last seven minutes to verify Bombelli's result were just what I wanted to see: step-by-step from beginning to end. I watched another video where the completion of the process was "left as an exercise to the student." Okay, I *should* be a life-long "student." But at the moment, after a day of work and seeking informative diversion: a complicated and "complex" expression was claimed to resolve to a "real" number. Which made me wonder (but not enough to go through the arduous process just now): "Really?" The patient, clear, and calm answer was, "Yes, really ... and here is how it may be shown to be true."

[@bsul03420]

Many thanks to you professor Petra for a wonderfully clear series of lectures.

[@for-the-love-of-maths]

Wow This is how you introduce a topic,.. Thanks

[@ull893]

Best video on complex Numbers ❤Thank you.

[@Khwartz]

Hello Petra. I really want to say that You have a Really Good Didactic and that is Most Precious! :) You don't miss a pace, You refer to the History of the subject even without apparently falling in miss data and Your teaching is Clear and Calm. Wish You The Very Best In All Your Domains Of Life, for the Very Benefit You Provide For Free to the learner here! Best Regards, Didier

[@artsmith1347]

Calm. +1 ... also the rest, plus calm.

[@mnada72]

Thank you for the very nice video, I was looking for a complete set of videos for this topic. I started the video and all of a sudden, it ended, I discovered that 19 min has passed without I even notice. I really enjoyed, thanks.

[@johnq4841]

Thank you so much. I just cant stop watching your videos !!

[@SonuKumar-fm3jn]

i found it today and i am very excited to go through all these video. #thanks_you.

[@andreas3454]

Thank you. This series is simply invaluable.

[@20891]

Your English is very good

[@andrewfrankovic6821]

and virtually no German accent.

[@Mcsepps_Lamtbalps]

Her Maths is also very good

[@akash9818]

Thank you so much for this lecture. I've always been extremely interested in complex analysis but I've never found any courses online that go sufficiently deep enough whilst still being extremely accessible.

[@chasr1843]

Well I just watched the last two vids in this series concerning the zeta function, prime number theorem, Riemann hypothesis. They I great! Petra can explain in two 20 minute vids what others take hours to try to explain and then they only confuse things. Now I'm gonna watch the whole series. Thx Petra :)

[@davidjones5319]

Awesome series

[@sukursukur3617]

I like to see thinking style of inventors. I like to see reason of rise of idea. And i am curious about their reactions in when they see the point that complex numbers have reached

[@Labs51Research]

Thank you for making these videos! Brilliant

[@lateefahmadwanilaw8948]

Amazing. Thank you ma'am

[@aditiyadav3482]

Ma'am your teaching is really really nice ☺ pls continue to teach like this only

[@monoman4083]

very good and helpful. thanks.

[@abajabbajew]

11:54 This equation has a different form that in the previous slide. I see that it is a rearrangement of the first however and therefore it's equivalent.

[@mu.makbarzadeh2831]

I love this course!

[@kachunli9853]

very good about this algebraic logic

[@husseinshimal7567]

Hey. Your 30 lectures about complex analysis are great. Why you stopped posting more lectures?

[@satyabrataghosh703]

Thanks a lot for this video...

[@liugng71]

Amazing demo on the first early use of imaginary numbers.

[@kaiz8597]

I don't know how to thank u , I was really interested in seeing and learning this topic in depth. So thank u again

[@UnbeknownToHis]

Amazing, Amazing, Amazing.

[@ouafieddinenaciri3783]

Thank you professor for this course .. I really enjoyed and appreciated the historical introduction to the subject .. I would like just to notice that when resolving the equation x cubed = 15 x + 4 you used a formula containing + between the two cubed roots instead of the "minus" in the general formula given before for the equation x cubed = p x + q .. Of course the square root of - 1 will cancel anyway but I think there is here some incoherence because we were supposed just to take a special case and use the previous formula not a new one .. What do you think ?

[@waynemv]

Petra, thank you for sharing these. I've watched the first three weeks worth. It's fascinating and (so far) easy to follow. 1) Is there a proper KZbin playlist for this series? I didn't find one, and so I had to hunt for each video in the series when watching them. 2) How many weeks/videos is this series in total? Is this series complete, or are you still adding more videos? 3) Do you have any short problem sets or self-tests for viewers to check their comprehension against? I have formal training in Calculus, introductory linear algebra, and introductory linear equations, but not in complex analysis, or any other higher maths. Awhile back I was trying to read through "The Road to Reality" by Roger Penrose. I started getting partially lost when Penrose was talking about complex numbers and homologous functions, so I set the book aside. But now I think I'll be able to breeze through that portion of Penrose's book once I finish your video series. Also, I had started watching a different series of videos on complex analysis before I found yours, but that one got too difficult too quickly. I found your videos through a comment another viewer left there, recommending everyone watch your series first. I also plan to go back to that other series after I finish yours. It is "2069 Complex Analysis" on the channel "MathsStatsUNSW".

[@hubercats]

Very helpful. Thank you!

[@barryhughes9764]

Wonderful to know such intellect exists. There is hope for mankind after all.

[@macbethsancar3418]

That was amazing.

[@2010RSHACKS]

Thank you so much for this course! My university doesn't have a complex analysis course and I really wanted to take one!

[@sguzzygang]

Amazing! Thank you!

[@gustavobagu7156]

Superb lectures!... Thanks Petra!

[@kurono1822]

These videos are too great and somehow buried in youtube

[@davidjones5319]

Mr Taylor is a lucky man.

[@varmanishant]

Thanks. How did Bombelli figure out that "2 + i" could be the cube root? Was it a "wild thought"?! He must have been like his contemporary Nostradamus :-).

[@mahamoodkuniyil9330]

fantastic. thank you!

[@venelinpetrov6811]

I kind of disagree that greecs "knew all this", because graph plotting wasn't discovered up until Rene Descartes. He introduced the Cartesian coordinate system for the first time

[@abcdef2069]

can you explain more about how prime numbers got related with a bunch of series?

[@shyamdas6231]

Thank you.

[@martingutlbauer4529]

Is there a script available to follow your course?

[@abcdef2069]

del ferros's cube eq was intentionally changed to have 1 solution. what happened to the 3 solution cube eq? who solved it ?

[@fareedullah1884]

Mam please upload more lecture love from pakistan

[@YoungLink51423]

Anyone know where I can download the slides?

[@AakarshNair]

great!

[@dobosattila3855]

Thank U for the lectures Good Job!

[@trevorsimpson8788]

i need to seek out these persons who have disliked these videos

[@adivasi6894]

The Wesleyan people still bitter she left them for Dartmouth.

[@maxim9976]

Thank you for this great video. I have a small question. x^3 and 15x+4 have three intersection points. Why does solution in video give only one intersection point?

[@crittinger]

Probably because they are irrational and not very pretty, and the point of the video is not to find all solutions but to show that at least one solution always exists

[@maxim9976]

@@crittinger I've been waiting for this answer for five years :=)

[@devjyotimondal1466]

The formula given to find the roots of a cubic equation. How do we get 3 solutions from that formula when the two intersect at 3 different points?

[@alnath_engore]

I hope you have gotten your answer by now. If not, well then the issue is:- The n-th root of r*(cos theta + i*sin theta) has n solution (complex numbers in general). So in the Bombelli's problem, indeed you have three values for (2 + 11i). There are also three solutions for (2 - 11i) which are complex conjugate of the previous three solutions, thus if you add them, you get all 3 real solutions. However, this needed more exploration of the properties of i (especially the fact that there are n-solutions for n-th root of any complex number). Such a property could not be derived solely on algebraic manipulations like Bombelli did. Obviously he couldn't figure it out. If you are curious, the 3 solutions of (2+11i)^(1/3) are sqrt(5)*{cos(phi) + i sin(phi)}; sqrt(5)*{cos(2pi/3 + phi) + i sin(2pi/3+ phi)} and sqrt(5)*{cos(4pi/3 + phi) + i sin(4pi/3 + phi)}; where phi is 1/3*arctan(11/2). The solutions of (2-11i)^(1/3) are just the above solutions with i replaced by -i (complex conjugate). Adding them, gives you your desired 3 solutions as, 2*sqrt(5)*cos(1/3 arctan(11/2) ), 2*sqrt(5)*cos(2*pi/3 + 1/3 arctan(11/2) ), 2*sqrt(5)*cos(4*pi/3 + 1/3 arctan(11/2) ). Type them in your calculator to see if you get what you expected ;)

[@MathCuriousity]

@@alnath_engore How did you bring trig into this? Can you please provide logic for this and the formulas used?

[@MathCuriousity]

@@alnath_engore so I am confused. In total how many REAL solutions and how many COMPLEX?

[@MathCuriousity]

Can someone please tell me how she got this form of the quadratic. Even after I took the usual formula we learned in school, and took her variables and order and fit it into ours, I end up getting m/2 +/- square root((-m)^2 + 2b))/2. I dont understand how she got m^2/4 + b

[@kyklous3657]

According to the quadratic formula, you would get (m +/- sqrt(m^2 + 4b))/2 (reminder that (-m)^2 = m^2). All she did was put /2 into the radical, so it would be the same as saying sqrt((m^2+4b)/(2^2)). Final result would be m/2 +/- sqrt(m^2/4+b)

[@theultimategamming3126]

if there will be tutorial with solving question ,it will be better to understand.

[@omnibrain8]

Please the solutions to quadratic and cubic functions have two and three solutions respectively. I want to know why with the formula for the two different functions gave a single solution?

[@kenbob1071]

A quadratic equation has at *most* two solutions.

[@darrenpeck156]

Thank you

[@samreenfatima6646]

Assalam u alikum

[@samreenfatima6646]

Ap complex analysis ki application ki video ha kea youtube pr

[@edmann19592000]

brava!

[@simeyD]

Zee Zee Zee.!!! Born in Germany it is pronounced Zed.!!! Reeman, NO Reimann!!.

[@oldcar8592]

His name is spelled Riemann so I think 'Reeman' is the correct pronunciation which is what she says.

[@cn96]

@@oldcar8592 i like to pronounce it like ryeman. it makes me think of canadian whiskey, Rye, Which makes me happy.

[@theultimategamming3126]

if there will be tutorial with solving question ,it will be better to understand.