Maths with Complex Numbers
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- čas přidán 26. 06. 2020
- How the Fourier Transform Works, Lecture 5 | Maths with Complex Numbers
Next Episode: bit.ly/3kFRMMH
Course playlist: bit.ly/2WyzWD4
howthefouriertransformworks.com/
View the whole series at: • Understand the Fourier...
The mathematical beauty of ‘i’, the square route of minus 1, is all very well, but what use to us is a number that cannot be calculated? Well in the Fourier Transform, ‘i’ serves a very important purpose indeed. It keeps things separate, and that is exactly what we want from an algorithm that breaks a signal apart into its constituent sine waves. How does ‘i’ keep things separate and how does this help us?
This is the seventh in this series of videos which take a new and visual look at the maths behind the magic of how the Fourier Transform works.
Please help me finish filming the course by supporting me on Patreon: www.patreon.com/MarkNewman
A transcript of this lecture can be downloaded from the following link:
drive.google.com/file/d/1wIX6...
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Thanks for watching the video How the Fourier Transform Works, Lecture 5 | Maths with Complex Numbers
after countless hours trying to understand Euler’s Formula and the imaginary plane I vote this as the most effective and accessible learning resource. It will be a crime if this doesn't end up with the same (or more) views as some of the big names out there (Mathologer, 3Blue1Brown, etc)
I'm SO glad my videos helped you. I always found complex numbers SO confusing at University and it took me years to understand what was going on. (I'm still of that journey of understanding even today). I'm working on trying to get the videos more views. If you could share them with whoever you might think would benefit from them then that would be a real help to me. Thanks.
Wonderfully explained concepts. Everything from the thorough explanations to the visuals are clear. Thank you.
Best by far, this man teaches these maths concept in the most intuitive way.
Thank you. That was my aim. I have always found mathematical explanations rellying on the manipulation of equations a challenge to understand.
I love how you don't leave any stone unturned when trying to explain something, its always easy to skip something you know well however when you haven't always got the best basis foundation of knowledge this type of explanation from almost first principles is brilliant, thank you.
This whole series is excellent; takes you step by step from the simple to the complex. Thank-you.
Incredible! Many people seems to gloss over the detail of how the cartesian form developed into the polar and doesn't even tell why each have it's own perks. Hopefully you'll get the recognition you deserved!
Thank you for your kind words.
An outstanding visual explanation of the Fourier Transform. The visuals really help to develop an intuition of the concept and in my opinion that's a big "missing piece" of the standard way of teaching this and similar concepts/ideas at a university. Thank you very much for the effort.
You're most welcome. I always needed the diagrams when I was learning this at uni and no-one was drawing them. Everything was always explained only with equations, so I thought that I'd better do the diagrams instead.
I enjoy these visual presentations! Learned a lot! 😊
WOW, you are incredible ! Thank you for this superb explanation !!
Such a great explanation. You have a gift for teaching complex subjects.
Wow, thank you!
This is not only awesome but also excellent! Thank you Sir!
Absolutely brilliant! What a wonderful exposition. Thank you again, my good man.
You are most welcome. Suggestions for videos you would like to see would be gratefully received.
Perfect refresher, thank you.
Great work. Thank you sir for giving us this amazing content.
Can't wait for the final video! I'm glad you've stuck through on a 4 year project. It will help many people in the future.
Thanks. I'm still working on the course. Not giving up yet.
Thank you for making these amazing video!
Truly the most outstanding video I’ve seen so clearly explained and very interesting to watch. I’ve saved all your videos on my playlist on my channel. Thank you so much for these videos your teaching method is absolutely fantastic I really appreciate your videos 😊
Wow, thanks!
Mark Newman you’re welcome thank you 😊
Simply brilliant! Making the case for using the Euler equation to define any wave form. This is the foundation for understanding Fourier equation.
Love the fact that you're so passionate about complex numbers ❤
I am so glad your channel got suggested to me.
AN AMAGIN AND ETERNAL TEACHING. THANK YOU SIR, FOR YOUR SHARE OF CONTRIBUTION TO THE ETERNAL WORLD OF TECHNOLOGY.
Simply amazing!
great work continue
Thank you
Extremely clear explanation. Thank you
Glad it was helpful!
This is just Amazing. I have learn much today
Really glad to have helped. Please share.
Best videos about i I have ever seen.❤️
Great explanation... Now i got come clarity on these things... Thanks
You are most welcome
thank you!!
Sir Mark Newman, I thank you soooo much for " Math with Complex Numbers" video.
Great explanation , I started loving signal and system as an electrical engineering btech student!
Excellent presentation
Thanks a lot
You are most welcome
I thought complex numbers are just too hard before watching this one...no words to praise you sir... why such a quality video don't have many views...Ha ha .... I'm feeling for you
Thanks. I'm flattered you found the video helpful.
Great video work.
Thank you! I really enjoyed the technical challenges this video gave me.
Would you explain the other specific topic (quaternions). Thank you so much ,Sir Newman.
Amazing!
Glad you enjoyed it.
Superb presentation.
Thank you.
Awesome pictorial lecture. I enjoyed the three "Marks" at 9:00
Hah hah... Glad you liked it. I really enjoyed doing that shot. I had to think really hard about how to time it properly. I love the possibilities that the green screen process gives me.
Human thinking process is fragmented and in order to combine different concepts we have to come up with imaginary concepts which are definitely helpful if we have a hard defined objective.
Sir may be you are from 2040 i think nobody would have gone this much deep and you nailed it
V. Excellent video today I found on CZcams▶️...... ❤
I am also an electronics engineer..and understand the importance of the transform theories.. Thanks for such a nice explanations. Euler and Fourier would be happy with your work.😊😊😊
You are most welcome
By far one of the best explanations I've seen. Just a note, at 20:52, that should be 9-2i, instead of 9+2i, but it's corrected in the next slide. I was taking notes and saw that.
going on as ( - ) ...
You are great
Thanks. Really?? I'm just an engineer who has struggled with the concepts for his entire working life and has finally found a way of explaining them to myself. :-)
If we take e^(i.pi) +1=0 then we can eventually found e^(Pi/2) =i, how does this happend????????? Can you explain
Could any of this work in something other than base10?
Why did I not meet you 50 years ago when teachers who tried to explain these things to us students , because they did not understand what they were teaching us, made a pig's ear of their lessons and we dropped out.
Thank you for your kind words. You would have had trouble meeting me 50 years ago. I would have been -4.
@@MarkNewmanEducation 😂
Could anyone share the name of end credit music? It is very cool.
Thanks for your greatful explanation.
I can't understand those who made the dislikes
You're welcome
... I have been banging my head on this particular i/e/fourier/etc wall for months ... watched this video and for the first time perceived a faint glimmer of light in the distance ... gives one hope!!!
Glad to have helped you. This is one of my older videos. I have since learned more and made other videos on the subject. For example: czcams.com/video/3aOaUv3s8RY/video.html. Check out my channel for all my videos.
Some people call the vector a phasor. And as you progress along the θ axis a rotating phasor.
Great job explaining the deep insight of e^jt. How Mr. Euler had enough brain power to come up with this theory is a mystery. I think the significance of this imaginary number is no less than the discovery of relativity and quantum mechanics. Hats off to Mr. Euler! He commanded as much respect as A. Einstein did!
At 17:57, when you have 3/2i, why can't we just multipy that one term by i/i, which would give us -3i/2? I know it doesn't work out to the correct answer, but why is it wrong ?
Because you would have to multiply both numbers in the brackets by i. (9 + 2i) * i = (9i -2). You would still be left with an i in the denominator, it would just hop onto the 9 rather than the 2. The beauty of the complex conjugate is it totally cancels all the i's in the denominator.
Nothing wrong with multiplying by i/i to simplyfiy 3/(2i) to -3i/2. The real issue is you can't FOIL division like he's showing. 3/(9+2i) does not equal 1/3 + 3/(2i)
In the complex plane you represent the imaginary unit i with length equal to the real axis unit. What's the reason for that? I mean, i=sqrt(-1) and real axis unit is 1. So, are you implying that sqrt(-1)=1?
OK. A CN's general form is a+bi where a and b are real numbers and bi is considered to be the imaginary part. Right? How do you know that multiplying a real number with the imaginary unit results in an imaginary number?
Excellent I will support
Bill in Aus
Thank you so much
fine
May be my ignorance.Are the angles in this equations measured in radians.Just curious
Yes. The natural way to express angles with sines and cosines is in radians.
@@MarkNewmanEducation thanks for clearing
@@MarkNewmanEducation So why does the presenter say "degrees"?
6:26 the angle should be theta+53.1 degrees, not theta-53.1 degrees
I can understand adding two complex numbers. But what does it mean when we multiply complex numbers. I thought the purpose of "i" was to keep the real and imaginary parts separate, because they are on two separate axes and that makes sense. Yet why we mix up the imaginary and real numbers in multiplication process. In another word the real parts can increase the size of imaginary parts. Further I can't see grphically the effect of multiplying two conplex numbers, and why we do that and what is the use of resulting complex number and what it represent in physical world.
Adding of complex numbers can be thought of as a translation on the complex plane, multiplying as a rotation (+scaling). If you do a search on CZcams for "visualisation of complex multiplication" I'm sure you'll find some helpful content.
Hi Mark. Is there a lecture 4? Am I missing one?
czcams.com/video/sKtloBAuP74/video.html
Yes. Lecture 4 has been out for some time. It was the first one I actually filmed. czcams.com/video/sKtloBAuP74/video.html
czcams.com/play/PLWMUMyAolbNuWse5uM3HBwkrJEVsWOLd6.html. This is a link to the complete playlist of all the available lectures.
I wish I had even only a fraction of your video-making skills :)
Wow. Thank you. I really enjoyed making this one. I'd just learned how to make 3D environments in my video editing software.
Fun times in math town.
Indeed
at 20:53 I think I spot a small mistake. The result should be [(3+4i)(9-2i)/85].
Woops! You are right. Sorry about that. Thanks for pointing it out. Fortunately, the mistake is only on that slide. It isn't carried forward in the working thankfully.
Complex nimbers are so beautiful
Shalom
Are you a professor ?
No, just a humble electronics engineer.
@@MarkNewmanEducation you are better than my univ professor.
You have the gift of teaching,
Iota nahi I cap
Good didactic structure of the lesson. But from the moment I notice your hat, I got so distracted and agitated that I couldn't finish the video. It is so terribly distracting, it destroys your whole effort for the video. Or did you plan to make the video for your religious community only? Then I obviously got the wrong video suggested. I detest religions which have the basic principle that they are the only right one and all others are obviously wrong. And people trying to spread those religions by displaying their symbol on the place that obviously needs to be looked at all the time. The same goes for cross around neck or headscarf. It's as if you tell everybody: see, I am part of this religion and if you are not, you are mistaken, because my holy book says so and it is never lying. I am usually agnostic as long as nobody tells me what I should believe. It's in those moments when I become Atheist. Are you aware of this effect? If not so, please notice that you are offending. If you are aware - well, you just proved me right.
I forgot there's a point here where he tells you to convert to his religion
See Cureyon if you are in any way offended I would suggest you to once and for only once read the holy books of all the major religions .
Also see the intro of his previous video of Euler Identity.
Hope this helps.
Complex numbers is fake invented math because
(1) the definition of a complex number contradicts to the laws of formal logic, because this definition is the union of two contradictory concepts: the concept of a real number and the concept of a non-real (imaginary) number-an image. The concepts of a real number and a non-real (imaginary) number are in logical relation of contradiction: the essential feature of one concept completely negates the essential feature of another concept. These concepts have no common feature (i.e. these concepts have nothing in common with each other), therefore one cannot compare these concepts with each other. Consequently, the concepts of a real number and a non-real (imaginary) number cannot be united and contained in the definition of a complex number. The concept of a complex number is a gross formal-logical error;
(2) the real part of a complex number is the result of a measurement. But the non-real (imaginary) part of a complex number is not the result of a measurement. The non-real (imaginary) part is a meaningless symbol, because the mathematical (quantitative) operation of multiplication of a real number by a meaningless symbol is a meaningless operation. This means that the theory of complex number is not a correct method of calculation. Consequently, mathematical (quantitative) operations on meaningless symbols are a gross formal-logical error;
(3) a complex number cannot be represented (interpreted) in the Cartesian geometric coordinate system, because the Cartesian coordinate system is a system of two identical scales (rulers). The standard geometric representation (interpretation) of a complex number leads to the logical contradictions if the scales (rulers) are not identical. This means that the scale of non-real (imaginary) numbers cannot exist in the Cartesian geometric coordinate system.