How do complex numbers actually apply to control systems?

แชร์
ฝัง
  • เผยแพร่เมื่อ 28 พ.ย. 2019
  • Get free access to over 2500 documentaries on CuriosityStream: curiositystream.com/majorprep (use promo code "majorprep" at sign up)
    STEMerch Store: stemerch.com/
    Support the Channel: / zachstar
    PayPal(one time donation): www.paypal.me/ZachStarYT
    This video mainly covers the underlying math behind the 'nyquist stability criterion' seen in control systems.
    Software Used in Video: www.desmos.com/calculator/
    Instagram: / zachstar
    Twitter: / imzachstar
    Join Facebook Group: / majorprep
    ►My Setup:
    Space Pictures: amzn.to/2CC4Kqj
    Magnetic Floating Globe: amzn.to/2VgPdn0
    Camera: amzn.to/2RivYu5
    Mic: amzn.to/2BLBkEj
    Tripod: amzn.to/2RgMTNL
    Equilibrium Tube: amzn.to/2SowDrh
    ►Check out the MajorPrep Amazon Store: www.amazon.com/shop/zachstar

ความคิดเห็น • 204

  • @starryfolks
    @starryfolks 4 ปีที่แล้ว +247

    3blue1brown animation on point

  • @matthewadamsteil
    @matthewadamsteil 4 ปีที่แล้ว +316

    When i got into college i was absolutely shocked at how imaginary number were SO useful! Videos like this brings me inexpressible joy.

    • @JulieanGalak
      @JulieanGalak 3 ปีที่แล้ว +3

      I didn't discover that fact until long after college. In large part thanks to videos like this.

    • @yosefmacgruber1920
      @yosefmacgruber1920 2 ปีที่แล้ว

      The difference between a blah calculator and a cool calculator. Whether it has *_i_* on one of its buttons. Even if you have to _shift_ to get to it.

    • @abhinav3478
      @abhinav3478 ปีที่แล้ว

      i didnt get why 'i' is so very useful or why 'i' is needed even at college. other than using it in every equation i use :|

  • @karimkhazaby
    @karimkhazaby 4 ปีที่แล้ว +143

    As Feynman said: if u want to master something, teach it. So I think your teaching technique is really awesome. Well done. Thank you so much. Great respect for you and your endeavour👏👏👏

    • @johnjacobjinglehimerschmid3555
      @johnjacobjinglehimerschmid3555 4 ปีที่แล้ว

      Hmm didn't know that. Found it out in my first chemistry course. Worked in a group after class and .... found that as I explained something I knew other stuff made sense and I was able to get more from the class if I helped others by explaining something.
      Unfortunately, next semester of chemistry nobody wanted to have a study group and man did I struggle. Still was one of the students that was doing well, well enough for the teacher to ask myself and another if we'd tutor in the study lab, didn't feel comfortable for someone to come looking up to me to give them an answer. But I agree ... you want to learn something ... teach what you know other stuff from the fringe will make sense ....

  • @swamihuman9395
    @swamihuman9395 9 หลายเดือนก่อน +5

    - Thx.
    - I took controls in college, and studied zeros/poles, and Nyquist - BUT, was presented a largely procedural understanding, though did include concept of stability, of course.
    - Years later, I became a math teacher... and I love the underlying insight provided by including mathematical view. And, I think this thinking could/SHOULD have been included in the engineering course.
    - BTW, I experienced the same joy of insight when i revisited the Fourier Transform and discovered the idea of an Integral Transform, and how a "spinning" kernel teases out the frequency components - and how a particular kernel results in the Laplace Transform.
    - The takeaway: the generality, and insight of math is very powerful! :)

  • @dineshpooja1969
    @dineshpooja1969 4 ปีที่แล้ว +28

    Eagerly waiting for fourier and Laplace videos !!!!!!!!!!

  • @eggyrepublic
    @eggyrepublic 4 ปีที่แล้ว +60

    Do I find this cool? Yes.
    Do I understand how it works? Absolutely not.

  • @QYong-rq6iw
    @QYong-rq6iw 4 ปีที่แล้ว +22

    When I was in a Controls class I couldn't understand or appreciate shits because it was just statements that got thrown at my face. Not sure whether it was the lecturer or myself who was incompetent and brain fogged. Now watching your video finally made me appreciate something, even though I am not bothered yet to really pause and ponder in order to more fully understand the stuff.

    • @Embracing_Impermanance
      @Embracing_Impermanance 4 ปีที่แล้ว +1

      Same thing happened to me bro I wish this video had come 3 years early

    • @bikerfirefarter7280
      @bikerfirefarter7280 3 ปีที่แล้ว +2

      Lecturer. They can demonstrate they know how to do something, but they do not explain the underlying thinking.
      Most are guilty of it. Some just don't realise, some do it to gloat and they don't want competition, and the dumber they keep students the more secure their posts due to demand/'re-takes'; trust me, as a technician I've seen and overheard this often enough.

  • @shohamsen8986
    @shohamsen8986 4 ปีที่แล้ว +15

    When I learn control theory, we sort of skipped all of this and went directly into the modern theory of control ( at least that's what I think it's called). Everything is dealt with using Lin ear algebra. It's nice to get to know these topics, because it wasn't covered in my control course

  • @zyzzbodybuilding
    @zyzzbodybuilding 4 ปีที่แล้ว +18

    Man ive been watching your vids since you had like 3k subs making those computer science course outlines. You have come a long way and the content keeps getting better. LV you dude, your also a good looking guy

    • @zachstar
      @zachstar  4 ปีที่แล้ว +1

      Thanks for sticking around man!

    • @bikerfirefarter7280
      @bikerfirefarter7280 3 ปีที่แล้ว

      @@zachstar "previously on complex number stuff". NO BLOODY LINK!
      Tchah! What's the point of mentioning it if there is NO LINK?

  • @SKARTHIKSELVAN
    @SKARTHIKSELVAN 4 ปีที่แล้ว +2

    Thanks for putting lot of efforts in making these videos.

  • @alexramirez5104
    @alexramirez5104 4 ปีที่แล้ว +1

    Perfect timing...we are studying this concept right now in my Control Systems class...thanks!

  • @kaleevans1692
    @kaleevans1692 4 หลายเดือนก่อน

    Great video. Awesome discussion and your an amazing talent at showing the math graphically and with the right timing and explanation. Keep up the great work!

  • @rakshithramesh4333
    @rakshithramesh4333 4 ปีที่แล้ว

    Awesome! Really helped me the meaning behind the Nyquist plot to determine stability of closed loop system. Thanks a lot !

  • @saifikhan5936
    @saifikhan5936 ปีที่แล้ว

    Superb video 😍 very conceptual. Highly appreciated your efforts ☺️

  • @PenguinMaths
    @PenguinMaths 4 ปีที่แล้ว

    Wonderful video with great visuals.

  • @kaustubhsalve9047
    @kaustubhsalve9047 4 ปีที่แล้ว +61

    Man you should have put this a week earlier. I had my test back then

    • @AnujShahshahmanuj
      @AnujShahshahmanuj 4 ปีที่แล้ว +6

      Yeah same! A few days ago I had an exam on Control Systems, and they asked the question:
      "Explain the Nyquist Stability Criterion."

    • @thatkindcoder7510
      @thatkindcoder7510 3 ปีที่แล้ว

      @@AnujShahshahmanuj Big oof

    • @puddleduck1405
      @puddleduck1405 2 ปีที่แล้ว

      bro same my test was yesterday

  • @cosmicvoidtree
    @cosmicvoidtree 3 ปีที่แล้ว +3

    Just for those curious, if you want too do these functions in desmos, the z squared formula is (a^2-b^2,ab) and to add 5 for instance just add a +5 in the x coordinate. For any function, evaluate the the formula then reduce i's (making i^2 into -1) until you have either 1 or 0 i's in each term. For example: a+bi+ci^2+di^3+ei^4 (in this case c and e are being used as variables not as the speed of light and Euler's number), a has no i's so we ignore it, +bi has 1 i in it so we ignore it for now (do remember that it has an i on it as that will be important later), for +ci^2 we cut out the i^2 and make the plus sign a minus sign: +ci^2 --> -c, for di^3 remove 2 of the 3 i's to get -di, and for ei^4 the two pairs of i's cancel to make 1 so it gets converted to e. Taking all of the converted terms you get a+bi-c-di+e, for reasons you'll see next step, lets rewrite it as a-c+e+bi-di. Now put parentheses around it: (a-c+e+bi-di), switch the sign before the first term with an i component with a comma: (a-c+e,bi-di), and completely remove the i's (a-c+e,b-d), don't compensate for them just cut them out entirely. And you've got your point You can substitute any value for the variables, add more or less, make them all only depend on two variables whatever. If you read all this then either: You are a nerd like me, you want to do what I just taught you, or you're someone who is reading this as a challenge or something. Anyway thanks for reading this and later I might add a link to a desmos graph which shows off this.

    • @lih3391
      @lih3391 ปีที่แล้ว

      Isn't it (a^2-b^2,2ab)?

  • @sujaypoudel4694
    @sujaypoudel4694 4 ปีที่แล้ว

    Excellent !! Loved it

  • @KaustavMajumder
    @KaustavMajumder ปีที่แล้ว +1

    Man, I wish I could actual take live lessons from you! You sir, are amazing!

  • @atriacharya2967
    @atriacharya2967 4 ปีที่แล้ว +6

    Thank you so much, sir. I am a third year electrical engineering student and the last 2 videos have been so very much useful for my broader understanding.

    • @lifehope4201
      @lifehope4201 3 ปีที่แล้ว

      In which college you are...

  • @fgcg4448
    @fgcg4448 3 ปีที่แล้ว

    Thanks a lot for this amazing explanation !

  • @TaladrisKpop
    @TaladrisKpop 4 ปีที่แล้ว +2

    The contour method is simply seeing complex functions as vector fields, but the visualization is really nice. It shows how computers can really helps in mathematics

  • @prajeethkodru1930
    @prajeethkodru1930 ปีที่แล้ว

    Thanks a lot for making this video!!

  • @jamesbra4410
    @jamesbra4410 4 ปีที่แล้ว +8

    Your channel is much better and more useful than 3Blue1Brown or any other math/engineering channel. I took complex variables and this video basically substituted the entire class into one it was so comprehensive. Of course minus the residues, complex logarithms, cauchy's formulas, triangle inequality, bounded functions, gamma function, inverse Laplace residues, improper fourier integrals, bessel coefficients etc.

    • @shambosaha9727
      @shambosaha9727 4 ปีที่แล้ว

      3b1b fans: TRIGGERED

    • @aaAa-vq1bd
      @aaAa-vq1bd ปีที่แล้ว

      Triangle inequality should be taught at the very beginning of any analytic geometry course, no?

  • @madaaz6333
    @madaaz6333 4 ปีที่แล้ว

    It's a beautiful work!

  • @manavrevaprasadu
    @manavrevaprasadu 7 หลายเดือนก่อน

    This guy loves springs so much he puts it in every video

  • @xiaosun9111
    @xiaosun9111 4 ปีที่แล้ว

    i finally got it!
    great video, thanks!

  • @davidpalmer9780
    @davidpalmer9780 4 ปีที่แล้ว +17

    I'd like to see you discuss Kalman Filters, in another video, given their control functionality.

    • @rulisastra
      @rulisastra 4 ปีที่แล้ว +2

      Unscented kalman filter too, since it uses sigma points

  • @DiegoMathemagician
    @DiegoMathemagician 4 ปีที่แล้ว +1

    I love your recent videos

  • @dakrontu
    @dakrontu 4 ปีที่แล้ว +2

    The math of complex numbers and Laplace transforms etc is beautiful but I am so glad I took the digital electronics option rather than more control theory.

  • @tollsimyfpv
    @tollsimyfpv 3 ปีที่แล้ว

    Wow! So illuminating.

  • @irelandtamilandamo
    @irelandtamilandamo 4 ปีที่แล้ว

    Wow. ! I can master control systems thru your videos. Thanks man !!

  • @aks9545
    @aks9545 4 ปีที่แล้ว +8

    It would be cool to have an app where you can put a complexe function and draw your inputs and see the outputs

  • @bachirblackers7299
    @bachirblackers7299 3 ปีที่แล้ว

    Best video ever !!! Gud job prof !!!

  • @shiroharra3058
    @shiroharra3058 4 ปีที่แล้ว

    i love this channel

  • @WolfrostWasTaken
    @WolfrostWasTaken 4 ปีที่แล้ว

    Brooooo when you started talking about Control Systems I was like "wtf this is so useful!!!" holy

  • @mridulnatani
    @mridulnatani 4 ปีที่แล้ว +11

    If you had released this video 5 days before, I would have got an A in controls 😅😅

  • @housseinnaserdine5874
    @housseinnaserdine5874 2 ปีที่แล้ว

    very amazing animations

  • @Topspeedcraft
    @Topspeedcraft 11 หลายเดือนก่อน

    I watched this video after watching one named "all you need to know about control theory" by the Matlab channel. I took a complex analysis class in eng major and i never fully understood all the praising my teacher did for the use of complex analysis in control theory. After watching the video i just mentioned, I commented that i would have liked to see some complex analysis there, and now just finishing watching this one.
    I can say that they complement each other quite nicely so i recommend you watch the one posted by Matlab. It's quite interesting to see how the feedback and feedforward theories relate to the stability and creating new dynamics in the system regarding the graphic insights provided by this video. Also you can see a clear connection with one of the key premises of the "All you need to know about control theory video" which is that you don't need to measure the state of the system to know what inputs would look like if you made a disturbance or shift.
    You can just observe the behaviour on the simpler open loop system and use nyquist criteria to determine stability of the more complex closed loop system with feedback.
    This is an amazing video and takes care of a quite interesting topic in a quite digestible way, took me a semester to learn what this video renders just over a dozen minutes. Beautiful work, the dedication and attention to detail shows, this is work well done. Thanks a lot

  • @dozog
    @dozog 4 ปีที่แล้ว +2

    As i said last time. Your script is really good.
    The speed may be a bit fast for new learners to pick up all the details,...
    ...it is really, really good as an introduction, a refresher or a summary.
    (which you don't get if you go slower)

  • @bionic5059
    @bionic5059 4 ปีที่แล้ว

    That refreshed some horrendous memories from the control systems course ...but thanks..i never understood it during my time at the university, I just applied it.

  • @calebsherman886
    @calebsherman886 4 ปีที่แล้ว +1

    I was completely lost this entire video, and at first I was kinda sad because this is something I wish I knew more about. But then I realized it's a good thing because before this video I didn't know what I didn't know.

  • @andy_lamax
    @andy_lamax 4 ปีที่แล้ว +2

    Wooooow!! I thought I totally understood my control systems class

  • @k.c.sunshine1934
    @k.c.sunshine1934 4 ปีที่แล้ว +1

    I studied Electrical Engineering 30 years ago. With this video, I have new intuitive understanding of the stability of control systems, etc.
    Thank you!!! This presentation video is cool!

    • @atriacharya2967
      @atriacharya2967 4 ปีที่แล้ว +1

      My god, a 50 yr old man watching technical videos!!!

    • @k.c.sunshine1934
      @k.c.sunshine1934 4 ปีที่แล้ว

      @@atriacharya2967 HaHa. Funny.
      This time and space in life is one of endless learning.

    • @atriacharya2967
      @atriacharya2967 4 ปีที่แล้ว

      @@k.c.sunshine1934 what do you do for a living, sir?

    • @k.c.sunshine1934
      @k.c.sunshine1934 4 ปีที่แล้ว +2

      I'm retired from engineering, however, I am still fascinated with technology. My engineering career forced me to constantly read and improve and I maintained the habit into "mid-life." Now that I'm hooked on learning, I will likely continue learning 'til death.

    • @atriacharya2967
      @atriacharya2967 4 ปีที่แล้ว +2

      @@k.c.sunshine1934 that's great to know, sir. All the best👍💯

  • @TheBeatle49
    @TheBeatle49 4 ปีที่แล้ว

    This gives me glimmer of understanding what I didn't get as a math major.

  • @Binyamin.Tsadik
    @Binyamin.Tsadik 4 ปีที่แล้ว +4

    Yes, thank you!
    Go deeper on control systems please!

  • @joyride6062
    @joyride6062 4 ปีที่แล้ว

    Literally did Nyquist criterion in my controls class today and didn't understand a dam thing. You just saved my midterm

  • @L0j1k
    @L0j1k 4 ปีที่แล้ว +22

    Hell yeah. 10/10!

    • @Christopher._M
      @Christopher._M 4 ปีที่แล้ว

      How come it says one wee ago

    • @adityams1659
      @adityams1659 4 ปีที่แล้ว +2

      exactly!!
      i guess a patreon

    • @hansisbrucker813
      @hansisbrucker813 4 ปีที่แล้ว +4

      Wait 10/10! is a really low score 🤔

  • @ajaysinha5803
    @ajaysinha5803 4 ปีที่แล้ว +3

    Well.... As far as i know.... The input which goes throuh a complex function goes into the riemann plane which overlaps the origin 2 times(4D)... Giving an effect of going round the origin 2 times.....plz correct me if i am wrong

  • @kadironsel1913
    @kadironsel1913 3 ปีที่แล้ว +1

    Thanks for this Great explanation Zach. at 12:21 you said that the number of times the circles origin are same for both equations. N=Z-P . I am ok with finding "Z" and "P" . But how can we say the "N"s (number of circles around the origin) are same for both equations ? How did we get it?

  • @partialorder5596
    @partialorder5596 3 ปีที่แล้ว +5

    "If you want a real-world example of that, just imagine hypothetically that the spring constant were negative." LMAO

    • @ayushsharma8804
      @ayushsharma8804 8 หลายเดือนก่อน

      thats just an analogy, systems with 'negative spring constants' exist in real life, just try balancing a cone on its tip

  • @anandsuralkar2947
    @anandsuralkar2947 4 ปีที่แล้ว +18

    0:51
    Me:-tan'1+tan'0.5+tan'0.333

  • @-Rishikesh
    @-Rishikesh 3 ปีที่แล้ว

    14:42 this is great, but what if my function is not having a unit negative feedback, Should i calculate the correct cltf then reconstruct a oltf with unit negative feedback and then solve?

  • @da4mula885
    @da4mula885 ปีที่แล้ว

    14:52 nope. Im not in controls class, don't even do anything with math. But you explained it clearly. I honestly got sidetracked to this topic here, but I can see now how I can use it. Gonna use it for feedback signal flow for music programs. Which Gained my interest recently

  • @omri9325
    @omri9325 4 ปีที่แล้ว

    This reminds me of the amazing work in WelchLabs video about complex numbers.

  • @brogcooper25
    @brogcooper25 4 ปีที่แล้ว +4

    I wish I had these videos when I took controls 10 years ago.

  • @tejonBiker
    @tejonBiker 7 หลายเดือนก่อน

    Pretty neat explanation, zeros AND poles are constant topics and words in control theory, but never covered in this way .

  • @altuber99_athlete
    @altuber99_athlete 4 ปีที่แล้ว

    Another example of a unstable system is an electric circuit in which the Laplace transform of the output has poles with positive real part (i.e. they're located in the right-half side of the complex plane.) This is just like the example MajorPrep gave in the end, but I actually undertand it more: if the L.T of the output has a pole with real part, then the I.L.T. (i.e. the output in the time domain) will have a term with an exponential factor (to see this, recall the table of L.P. pairs and the partial fraction expansion.) Thus, if the pole has *positive* real part, then the exponential will have a positive exponent, for example y(t)=3e^2t amps. Notice that, as t increases, so does the output. What does it mean? After some time, the output current in the circuit will be huge! And we all know what high current can do.

  • @usmansaeed3662
    @usmansaeed3662 ปีที่แล้ว

    What software do you use for plotting the contours?

  • @realcygnus
    @realcygnus 4 ปีที่แล้ว

    superb

  • @happyhayot
    @happyhayot 4 ปีที่แล้ว

    Any recommendations for MOOCs in control systems?

  • @adrien5568
    @adrien5568 4 ปีที่แล้ว

    Can you put the link for the desmos graph ?

  • @NonTwinBrothers
    @NonTwinBrothers 4 ปีที่แล้ว

    Haha, nice use of Desmos!

  • @pasangtsering2380
    @pasangtsering2380 4 ปีที่แล้ว

    Which software you are using to show the graph???

  • @yvesdelombaerde5909
    @yvesdelombaerde5909 4 ปีที่แล้ว

    Plan complexe et courant triphasé: de grands souvenirs!

  • @devrajyaguru2271
    @devrajyaguru2271 4 ปีที่แล้ว

    Really helped me to get the best knowledge about imaginary numbers

  • @MusicEngineeer
    @MusicEngineeer 4 ปีที่แล้ว

    nice . looking forward to fourier and laplace transforms! ...maybe z-transforms also? (i'm a dsp guy :-))

  • @devrimturker
    @devrimturker 4 ปีที่แล้ว +4

    Excellent, everything in nutshell. May be a relation between mandelbrot set and nyquist added, nyquist seems shaved mandelbrot, leaving its fractals ;)

  • @The-Devils-Advocate
    @The-Devils-Advocate 2 ปีที่แล้ว

    3:34 can we say that since specific pairs of input points correspond to a single output in a square transformation, thus “halving” our number of “points” and “distance,” and causing the time needed to traverse the output contour to be half of the time needed to traverse the input contour?

  • @crawfordrhoderick2942
    @crawfordrhoderick2942 4 ปีที่แล้ว

    what calculator is the best to use for engineering.

  • @bhanusri3732
    @bhanusri3732 4 ปีที่แล้ว

    At 12:20 what does it mean the number of rotations for f(z) + 1 around 0 is equal to number of rotations for f(z) around -1

  • @user-gt2th3wz9c
    @user-gt2th3wz9c 4 ปีที่แล้ว +1

    Love u)

  • @thinkfirst6374
    @thinkfirst6374 3 ปีที่แล้ว

    This problem was in my highschool exam(12th grade) it was so easy, Greetings from Syria.

  • @mathscienceonlineacademy4512
    @mathscienceonlineacademy4512 4 ปีที่แล้ว +1

    Complex numbers is first chapter in our textbook of Mathematics.

  • @ajaysinha5803
    @ajaysinha5803 4 ปีที่แล้ว

    These types of vids really boosts my curiosity to the next lvl

  • @saido3278
    @saido3278 4 ปีที่แล้ว

    What software do you use for animation?

  • @jackwang862
    @jackwang862 ปีที่แล้ว

    Complex number gets both elegancy and pracitcal value.Awesome with inexpressible joy.

  • @fritschdavid
    @fritschdavid 4 ปีที่แล้ว

    I loved this so much. i have to see more of your world. This relationship of the untransformed vs. transformed make me think of a concept i am trying to understand: monads. which show up in leibnitz' philosopy, mathematics and as programming concept to e.g. deal better with empty values as far as i understood so far. I was shocked to see you are promoting nord vpn in another video. I intuitively know that this driven by Snodens former breadgiver. Nobody talks about the issue that using a vpn you make your internet access company unable to see the traffic, but you give whatever provider you choose full access to your stream of activity in all detail. i trust (at least a german) telecom much more to run their business according to the laws of data protection.. which of course is a european luxury. do you resonate with that?

  • @theperipateticaccrescent7685
    @theperipateticaccrescent7685 4 ปีที่แล้ว +3

    Can you make a video on comparing different types of majors and how much money each makes. I want to choose engineering for money and want to earn a lot of money (by business,start-up, entrepreneurship....etc). But am a bit unclear about how to go about it.

    • @univicta7212
      @univicta7212 4 ปีที่แล้ว +1

      Yes, please make a video on, Top Earning engineering professions
      (✯ᴗ✯)

    • @shambosaha9727
      @shambosaha9727 4 ปีที่แล้ว

      Money? AAAAAAAA...

  • @ganaieabdullah6713
    @ganaieabdullah6713 4 ปีที่แล้ว +1

    Can you make vedios on how to make audrino project

  • @nirgadish6573
    @nirgadish6573 4 ปีที่แล้ว

    I'm confused: the plot at the snapshot of the video - the green shaded region, that is the image of the interior of a rectangle surrounding both a zero, and a pole has 4 corners. They are the images of the 4 corners of the rectangle. BUT, why are the plotted corners not at right angles?! The image of a right angle should be a right angle. So what's going on with that plot??

  • @danielmalo1753
    @danielmalo1753 4 ปีที่แล้ว

    Don't understand half the concepts here but it's nice

  • @elkhayder
    @elkhayder 2 ปีที่แล้ว +1

    The first time i've seen those function and there plots in the systems control class ( asservissement ) I was like "they did not get enough with real functions, now they are drawing doodles"

  • @puddleduck1405
    @puddleduck1405 2 ปีที่แล้ว

    Im in highschool rn, and we've just finished the complex number topic. I didnt understand how they are useful in real life but this is so cool!

    • @ES-qe1nh
      @ES-qe1nh ปีที่แล้ว

      Yeah it's a bit of a jump from high school complex (de moivres, Euler's formula) to stuff like this (Cauchy, residue, integrals in C --> C) I'd say take calculus before you dabble in this if you want to absorb more knowledge

    • @puddleduck1405
      @puddleduck1405 ปีที่แล้ว

      @@ES-qe1nh ahh yes, in the UK we dont get a choice haha, we have to do calculus. ive never heard of Cauchy b4, it sounds interesting tho I might look into it!

    • @ES-qe1nh
      @ES-qe1nh ปีที่แล้ว

      @@puddleduck1405 Cauchy... Isn't a concept. I just quickly referenced it because of Cauchy's residue theorem in complex analysis. Obviously, Cauchy was a french mathematician and engineer.

    • @puddleduck1405
      @puddleduck1405 ปีที่แล้ว

      @@ES-qe1nh oh cool

  • @rulisastra
    @rulisastra 4 ปีที่แล้ว +1

    You're a genius. Why am I even here?

  • @charlesallan6978
    @charlesallan6978 ปีที่แล้ว

    We can use these theorem to mathematically transform the word 'though' into a useful form whence the g is pronounced instead of remaining silent and the ou becomes ow. Thence the h remains silent.

  • @Avighna
    @Avighna ปีที่แล้ว

    Here's how I solved the first angle question before watching the video.
    The sum of angles (via the pythagorean theorem / analytical geometry, whichever you prefer), which I'm gonna call S, is:
    S = atan(1) + atan(1/2) + atan(1/3)
    S = 45° + atan(1/2) + atan(1/3)
    S = 45° + atan(tan(atan(1/2)+atan(1/3)))
    S = 45° + atan( [ (tan(atan(1/2)) + tan(atan(1/3)) ] / [1 - tan(atan(1/2)) * tan(atan(1/3))] )
    S = 45° + atan( [ (1/2 + 1/3 ] / [1 - 1/2*1/3] )
    S = 45° + atan( (5/6) / (5/6) )
    S = 45° + atan(1)
    S = 45° + 45° = 90°

  • @JCisHere778
    @JCisHere778 4 ปีที่แล้ว

    How about complex potentials and conformal mapping to solve potential flow problems

  • @jewulo
    @jewulo 4 ปีที่แล้ว +2

    How did it get from 10i to 10exp((i * π)/2) @ 1:43? Sorry for my ignorance.

    • @happyhinoka8722
      @happyhinoka8722 4 ปีที่แล้ว

      using Euler's formula r(e^ix) = r(cos x + i sin x) cmiiw :)

    • @williamhensley8322
      @williamhensley8322 4 ปีที่แล้ว

      You need to foil the complex numbers in the video... The ones in the form of a+bi. There are 3 of them. You have to know how the imaginary component of the complex numbers are multiplied.

    • @jewulo
      @jewulo 4 ปีที่แล้ว

      @@williamhensley8322 What do you mean by foil the complex numbers?

    • @williamhensley8322
      @williamhensley8322 4 ปีที่แล้ว

      @@jewulo if a complex number can be defined as a + bi, then if you had to multiply 2 complex numbers, it would be in the form of (a1+b1i)(a2+b2i). Then you would multiply these two complex numbers in the same way you would multiply (x+1)(2x-2), multiplying the first terms, outside terms, inside terms, and the last terms and sum the products.

    • @williamhensley8322
      @williamhensley8322 4 ปีที่แล้ว

      Keeping in mind that an i^2 term is equal to -1.

  • @luxshokk
    @luxshokk 4 ปีที่แล้ว

    About the angles in the rectangle at the beginning: To be completely rigorous, wouldn't we have to acknoledge that technically, the phase of the resulting number could also be 90° plus any multiple of 360°? By adding angles together, you may, in general, indeed get a result over 360°. Is there a nice argument to show that it is indeed 90° and not 450°?

    • @nomechomath5644
      @nomechomath5644 2 ปีที่แล้ว

      Good question!
      If α, β and γ are all greater than 0° and less than 90°, then:
      α+β+γ > 0° + 0° + 0°
      α+β+γ > 0°
      and
      α+β+γ < 90° + 90° + 90°
      α+β+γ < 270°
      thus their sum is greater than 0° and less than 270°.
      That's how you can show that they must add 90° and not any other angle like 450°.

  • @adityams1659
    @adityams1659 4 ปีที่แล้ว +1

    hii
    Could you please please make a video on how you animate with desmos
    pleaseeeeeeeee!!!

    • @zachstar
      @zachstar  4 ปีที่แล้ว +3

      Not my next video but the following one is going to be involve a lot of animations that will be useful to those in a linear algebra class. I'm gonna make a separate video after that where I explain how I made that and I'll be providing the template I use so you guys can play around with it yourselves.

  • @jakoblenke3012
    @jakoblenke3012 4 ปีที่แล้ว +1

    Interesting how the bottom circle at 15:07 crosses the imaginary axis at sqrt(2)....

  • @mnada72
    @mnada72 3 ปีที่แล้ว

    Another great video. I was hapless to understand Nyquist Criterion but now the idea started to sink

  • @rikadomez8201
    @rikadomez8201 3 ปีที่แล้ว

    Whomever came up with the idea of square-rooting the negative 1 is simply genius.

  • @ckzslmr1405
    @ckzslmr1405 4 ปีที่แล้ว

    very nice explanation

  • @vatsan2483
    @vatsan2483 4 ปีที่แล้ว

    Hey dude.. can u make a playlist on channel that has all the videos for electrical engineers who have this one mandatory for their course.. this would be appreciated

    • @vatsan2483
      @vatsan2483 4 ปีที่แล้ว

      Like can u please group into one playlist.. with Laplace, Nyquist and alll..for easy accessibility.
      Thanks in advance 👍👍👍

    • @zachstar
      @zachstar  4 ปีที่แล้ว

      Here you go! I'll add more as they come.
      th-cam.com/play/PLi5WqFHu_OJN7Mb2aAgqcao2R3s9wbBEr.html

  • @Isaiah_McIntosh
    @Isaiah_McIntosh 4 ปีที่แล้ว

    Sigh gotta study math looking up.

  • @tafiqulrafi2569
    @tafiqulrafi2569 4 ปีที่แล้ว +1

    I thing I wanna ask u is why did u leave ur job as an electrical engineer?
    Well, I m in class 12 and next year I'll do undergrad in electrical engineering

  • @spazticle8752
    @spazticle8752 4 ปีที่แล้ว

    can you talk about engineering physics major

  • @anuzis
    @anuzis 4 ปีที่แล้ว +1

    Can you do a video on everyday applications of convex optimization? (not huge things like power grid optimization, but small every-day situations where humans could benefit from convex optimization if they were capable of doing it well)