EEVblog 1470 - AC Basics Tutorial Part 3 - Complex Numbers are EASY!

Complex numbers are NOT complex!
How complex numbers are used in AC circuit analysis.
00:00 - Complex Numbers
00:44 - Phasor graphical addition
01:22 - Why do calculators have the R-P and P-R buttons?
02:44 - Phasor diagram
03:59 - The AC voltage equation
04:47 - The complex plane and j vs i imaginary axis
06:21 - The Rectangular and Polar forms
07:36 - The j operator
10:38 - Polar and Rectangular format conversion
11:50 - Plotting points on the complex plane
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#ElectronicsCreators #tutorial

[@cinobro6393]

Would genuinely love a full fundamentals course. Imagine if Dave had a full EE course!

[@overengineeredinoz7683]

+1 for that.

[@bobvines00]

While Dave hasn't made such a course, there are quite a few here on KZbin. Since I haven't had much official (i.e., University-level) EE training (I'm an ME!), I looked and stumbled across the "Science and Math" channel where a guy who was a NASA EE teaches several free EE courses.

[@nameredacted1242]

Dig far enough, he had plenty of "courses" over the many years he has been making videos!!!

[@12kenbutsuri]

I will pay for that

[@techman2471]

Thank you, Dave , for these insightful instruction videos. I have been out of the AC power field for many years. It is good to have a refresher about complex numbers. I have been doing digital electronics and computers fro 20 plus years. In the US Navy, I worked on AC generators and motors, not really knowing this aspect expect for private study. Thanks again!

[@cinobro6393]

Thanks Dave!!! I can’t tell you how valuable this is for all electrical students!!!

[@JYelton]

I love the fundamentals and tutorials content the most! Teardowns, debunks, and mailbag are fine, too, but this is the stuff that I revisit, benefit from, and recommend to my colleagues.

[@mikegreen2079]

Another great tutorial, vital for both the new players and some old hands for a basics brush up over a coffee. Don't be disheartened by a few bad comments, your channel has something for everyone, after fifty years in the industry I still sometimes pick up a useful nugget from your content. Remember, you cannot please all the people all the time but I for one have watched your channel(s) for years, thanks.

[@polaraligned1]

30 years since I learned this in college. Never had a use for it in the real world, but neat to have learned it.

[@davidtodd7216]

We use j to avoid confusion with the symbol for current i

[@jvburnes]

This is awesome. 2 semesters of EE in 3 videos.

[@ValeraManasyan]

I absolutely love this explanation! Small mistake there though at 12:37 - it should be = -5 + j4

[@jimhark]

Thanks Dave, I love this content. Your clear and simple explanation really helped me bridge the gap between vector math (which I'm comfortable with) and complex numbers. Looking forward to more videos in this series.

[@Electrical-Engineering-Notes]

Lot to learn from this channel

[@TheArachnoBot]

Its probably "j" because "i" could be confused with current. Great video by the way, teachers as good as you are very rare and valuable.

[@SomeMorganSomewhere]

Loving this content, short punchy and gives you the info you need, as opposed to my university course (graduated some many years ago now) which padded this topic out to multiple semesters...

[@MrDoneboy]

I, for one, am a HUGE fan of these instructional videos, Dave. Thanks so much...you are appreciated!

[@bijayabaidya6896]

Brings back memories from 45 years ago! Well presented!

[@SaturnV2000]

Dave's enthusiasm is contagious!😀Keep up the good work!

[@tomasbergh]

After this Dave.... It is a must that you supply an ac voltage to an RL-circuit and measure phase and amplitude of the current and then compare to the calculated values. 😀

[@jkeelsnc]

Excellent presentation. Understandable and useful. You are a good teacher.

[@supernumex]

Great video! Can you do a series on AC power? (power factor, pfc, reactive power, THD, etc.)

[@MichaelLloyd]

I was literally just about to type that. His teaching method is so easy on the brain.

[@SaturnV2000]

Another way to express "CIVIL" as I was taught in college: "ELI" the "ICE" man . . . E leads I in L inductive reactance, and I leads E in C capacitive reactance. Since then, "V" has pretty much replaced "E" in electronics nomenclature . . . but still useful!

[@jcobnl]

Had a similar thing: LEICIE. I don't know if this is just a Dutch thing. L and C are inductor and capacitor, E is voltage (now U) and I is current.

[@johnp221]

Dave, Did this a long time ago at Tech and Uni but never had it explained as clearly as you have just achieved. Thank you.

[@mickeyfilmer5551]

Crikey- I never knew there was still so much to learn and, you make it easy to understand - Thanks Dave. I'm going to be binge watching your tutorials now.

[@nutsnproud6932]

Dave, thanks for taking the time t teach me something I struggled to understand for many years.

[@camk2552]

Lets get the smith chart out!!!!

[@tedcuff9155]

Good video Dave. I remember when I studied for AC analysis that the R-P P-R really made some of the calculations easier.

[@ericksonengineering7011]

Great video, Dave. Of the many ways to do AC analysis you nailed the most useful. I especially like your explanation of using polar for multiply/divide and rectangular for add/subtract, and the RP calc functions to convert. Details I've long forgotten since taught in the 70's and done on my HP45 at WPI.

[@Soapy555]

anyone else here just to look for the markbyeah comment?

[@EEVblog]

Looks like he deleted it.

[@TylrVncnt]

?

[@Qhotex]

Thanks for this, Dave!

[@tylerellis4576]

Thanks Dave! Always love your videos!

[@NamelesGhost]

Currently studying electrical engineering and this series is exactly what we learn in the basic courses!

[@movation]

Brilliant video Dr dave

[@davidgari3240]

So there is an application for imaginary numbers after all. Thanks for taking us back to school. Well done.

[@bynumite9361]

Got an A on my circuits 2 final!! I credit my success to you. Thank you!

[@johneverett5137]

great work Dave

[@HitAndMissLab]

Excellent video. Simple & practical. Thanks

[@prldh]

Great video Dave!

[@sarbog1]

Very cool! Complex numbers are a mathematical abstraction that model the real world... Very useful for Science and Engineering ! Remember j is for Engineers.

[@AvalancheBrkdwn]

Fantastic video, really liking the AC content, even as a refresher course for me. One question, however: at 15:12 you call the two components of the Polar form "Real" and "Phase Component". I think calling it Real can confuse some people because in Cartesian form, the Real part of the complex number is typically the x-axis, as you explained earlier in the video. Would it be better to call it "Magnitude" in this case?

[@Rene_Christensen]

Magnitude and phase, as you say, is correct.

[@Chrls5]

Dave , great at giving classes m8 🙏🙏

[@RagnarEE]

Yea, i just have to say... Damen, you are a SUPERB teacher Dave!! I got it!!👌👌👌👌👌👌😁

[@extremgear]

even for a french viewer like me this series of video is easy to understand, thank you .

[@allanoommenkurian9128]

Thank you Very much. Waiting for the next part 😀

[@highonpcbs]

Just started network analysys AC at university, as always very clear and helpfull!

[@DRawwrrr]

Thanks Dave!

[@Reapzorian]

Saw part 2 in my feed... missed part 3 somehow.. must have been busy. Lots of value in these tutorials to watch when I am able to focus on the video (as opposed to the 90% videos in the background while I work situation) Kind of surprising how low the view count gets when class is in session. Another possible angle - Many subscribers that would have watched this video may have already taken circuit theory :)

[@bigpips3051]

Got your note about the seperate channel. From here on, as soon as I get the bell notification i run your video, even if i have to come back and watch it later ;) shove it YT algorithm

[@theedspage]

Thank you for the great tutorial.

[@petercumiskey3188]

Good Video Dave. I now see (30 years later) were 2pifl and 1/2pifc comes from. Good on ya.

[@overengineeredinoz7683]

I wish I had this exact lecture during my University degree study. Great video Dave.

[@overengineeredinoz7683]

Hope you do exponential form too some day.

[@amnahaque9058]

My fav subject, back in 1999, while doing my Engineering degree.

[@keithminchin1817]

Really appreciate these tutorials. Great quality content. 👍🏻

[@KidCe.]

Leeeets goooo 😍😍😍 We just had this topic in school and this video video is gonna help me alot

[@niklasxl]

these videos are really great :D i would really like to see your explanation of Fourier transforms :D

[@stevedaenginerd]

OMG! Why couldn't my math teacher explain it like this?!😳🤓 The past 25ish years would have bee far easier if my Algebra teacher had explained it like this! Haha 😳 Thank you for putting this series out! It has answered a lot of questions I had on why A/C does what it does! 🤓

[@stevedaenginerd]

Also, would it be possible for a little followup with some practical examples? I thank you so much for all of the learnin' you've given me over the years!😜 Thank you! 🙏👍🤓

[@uwezimmermann5427]

Next week's program for me and my students! Good overview! If I want to be a bit picky than you should have indicated the phase in your sine-graph in the beginning between similar points om both waves, not between the falling slope of the blue and the rising slope of the red curve. Actually I never bothered to figure out R/P and P/R on the calculator, but always used (and taught) the "long" way using abs(Z) and arctan(Im/Re) - but now I will show my students what their calculators can do!

[@uwezimmermann5427]

20:56 actually it doesn't matter if you use rms-voltages, amplitudes or peak-to-peak voltages, as long as you stick one of these for the full calculation.

[@VandalIO]

زبردست وئڈیو ہے

[@TheTarkovish]

Thank you for these! Well, for most of your vids but esp for these ;)

[@scottholmes4388]

Keep making these Dave! Whiteboards FTW

[@MegaZiggo]

I need that shirt man...awesome!

[@mathr5255]

Fantastic!

[@petersage5157]

Obligatory dad joke: These phase components will always be Greek to me. Thank you for continuing this series, Dave. This is fundamental to analog electronics (which obviously includes audio). One thing that has always mystified me is exactly *why* there is a phase shift through a capacitor or inductor, and how voltage could possibly *lead* current through an inductor. Adding the complex dimension, it's actually starting to make sense.

[@McTroyd]

Pulled out my trusty decades-old TI-83 Plus, and had an existential crisis... it didn't have the R/P conversion buttons!! 😱 Crisis averted -- TI buried the functions behind the "Math" button (labeled ">Rect" and ">Polar" under the "CPX" tab). Whew. 😅 Oh, and thanks for motivating me to check the calculator... the batteries leaked. 🙄

[@jamesmorganonline]

After 10 or so years of watching this channel, I have never once left a comment. And the reason is simple. I enjoy Dave's content. The creator of this channel doesn't owe me anything and I have nothing interesting enough to contribute via a comment, so I don't. This message is for all the people that just can't help themselves but offer unsolicited advice on the types of output they feel there not getting enough of. You get what your given, and if you don't like it. Take your bat and ball and go home.

[@JoeMcLutz]

This is the case "Complex is simplier"... 😄Nice video as always, thank You! 👍🏻

[@youdontknowme5969]

OMG complex numbers fascinate me 😍

[@thomasgaliana6288]

I am here and I am watching! :)

[@davidwilkie9551]

Sort of remember this... Definitely recommend it to everyone in Science-Engineering.

[@matiasvlevi6647]

"j" is used in order not to confuse it with "i" which is current

[@olajonmann97]

Tank u

[@LawpickingLocksmith]

Angus from ACDC must be thrilled! C'mon play him in the background!

[@jcobnl]

I've had all these phase-shifting calculations at school (i work with low and high voltage electrical distribution systems, so lots of three-phase stuff like generators, transformers and networks) , except the polar/rectangular conversion. I always knew there was some sort of method to make these calculations easier, but somehow (i know, schooling level, i don't have a degree, i'm not an engineer) it fell out of the scope. I wish i had this knowledge much earlier before...

[@KeritechElectronics]

"Nothing imaginary about these numbers, they are very real" - haha, that was great! Catchphrase unlocked. 12:37 looks more like -5+j4 Again, complex is better than complicated! :D I like the CIVIL notation. Mnemotechnic to the rescue!

[@Gengh13]

Just supporting the algorithm.

[@pdr0663]

Dave, the reason j is used in favour of i is not “meh”, it’s because electrical engineers of course use i to represent current.

[@grattitudetebogo9501]

Awesome

[@SuperFinGuy]

I think complex numbers should be called compound numbers or multi-dimensional numbers. The complex name doesn't stand for complicated. Why i^2 = -1? Simply because i^2 = (0,1)*(0,1) = (-1,0)

[@kalli71]

brilliant! - i understand adding/substracting voltages, but why would we ever multiplyy/divide voltages (where does that occur?)

[@SkyhawkSteve]

Maybe I missed it, but I was expecting an explanation that i or j is the square root of negative one. It's been about 40 years since I had the class, but sometimes we had to multiply (a + jb) x (c + jd), and you had to deal with the square of j. Since j is the square root of negative one, the square of j is negative one, which is critical to getting the correct answers. Perhaps that is a bit deeper than this series of lessons was shooting for?

[@Asdayasman]

14:40

[@SkyhawkSteve]

@@Asdayasman but that doesn't address the need to do multiplication when you are still dealing with variables. In my example above, (a + jb) x (c + jd), the result is (ac - bd) + j(bc + ad). I can't imagine trying to do this by converting this to polar notation.

[@Asdayasman]

@@SkyhawkSteve I would guess that Dave, being an incredibly well experienced professional in the field, understands that the need to do that is rare enough that it doesn't need to be included in an "AC Basics" class. Remember he's a practical engineer, not a theoretical scientist. You can measure a whole bunch of stuff and reify a variable easily enough.

[@SkyhawkSteve]

@@Asdayasman this is first semester EE stuff... it's not hard. It might still be beyond what his audience is looking for, though.

[@Asdayasman]

@@SkyhawkSteve Sorry, I think you missed the part where I said Dave is a "well experienced professional in the field". I said nothing about the cesspit that is institutionalised education. 20% of the things they teach in universities are useless 80% of the time. The other 80% are useless 100% of the time. I don't care what's taught in the "first semester" - if Dave didn't see fit to explain it, it's not the sort of thing you need as a beginner.

[@tomas_soeterik]

PLEASE DO PART 4

[@Artichoke4Head]

Hey Dave, thanks for the great videos as always!!! when you said two adding sinwave always results in another sinwave, do they need to have Sam frequency?

[@EEVblog]

Yes, forgot to mention that.

[@Artichoke4Head]

Thanks! So if that's the case, if someone makes a very clever device to mix different sinwaves, they could theoretically make any other signal shapes like square, sawtooth or even DC from mixing sinwave? And also the other way around, you should be able to remove and separate this hidden wave shapes from example of a square wave? I'm not sure if what I said makes sense at all!😵‍💫

[@EEVblog]

@@Artichoke4Head Yes, that's called a Fourier transform!

[@Artichoke4Head]

@@EEVblog thanks for the answer and thanks a lot for your time and your video(s)

[@justina208]

I find Schwarzchild coordinates much more convenient :)

[@74HC138]

For multiplying them, wouldn't it be easier to FOIL the two complex numbers rather than converting to polar (especially if you have only a basic calculator to hand)?

[@JanCiger]

Complex numbers in mathematics are commonly expressed using i,j and k as complex ones, not only i. Essentially the Z = X + i.Y is the same as writing Z = 1.X + i.Y - vector addition of two components, where the 1 and i are unit vectors on their respective axes, only in practice 1 is omitted by convention. In higher dimensions (e.g. quaternions) i,j,k are used as unit vectors on the three imaginary axes.

[@josephfisher372]

Hi Dave, Your videos are very informative. I've learned a lot. Just a small correction to something that might be confusing to some viewers. On the diagram where you show the two sine waves against time, shouldn't the phase difference be shown shifted to the left between the downward crossings of the two waves rather than between the downward crossing of one and the upward upward crossing of the other as shown? (I know this is nit picking)! Thanks.

[@lucaeber2720]

When you add Voltages witch are phase shifted, you can add them in polar form with a calculator. Can a calculator do everything with both forms?

[@Adrian-Carstea]

Maybe it had been useful to introduce the exponential form too, to be able to explain easier the multiplication, division, power and root formula.

[@EEVblog]

I flashed that as an overlay at the end. Video was already a bit too long.

[@john_hind]

One correction Dave: On the diagram at 11:41, the whole diagram is the 'complex plane': a 'plane' is two dimensional. What you've labelled the 'complex plane' should be the 'imaginary axis' and the 'real plane' should be the 'real axis'. It's the real axis of the complex plane and the imaginary axis of the complex plane.

[@ProfMarcoCamara]

Dave, thank you very much for the video, but shouldn't the phase difference on the graph be measured between two ramps up or down? In your graph, the difference shown is between the fall of the reference signal and the rise of the other signal. Could you clarify this doubt?

[@Rene_Christensen]

You have spotted a mistake indeed. Also, the blue line should be a cosine, not a sine, since this is the real projection of a Phasor with angle zero.

[@karlm9584]

I've always wondered why complex numbers are used to describe vectors for AC power. There are other ways to do it. I suppose it is just more efficient?

[@LutzSchafer]

Dave you really kept it very simple in terms of engineering math. But you should have explained why j=sqrt (-1)

[@gregorymccoy6797]

Ronnie Coleman: Everybody wants to be an engineer but don't nobody wanna solve no heavy-ass equations.

[@sternobread]

You state "For addition and subtraction you need to use rectangular form. and for multiplication and division you need to use polar form". Is that strictly true? Can you not perform multiplication / division on complex numbers?

[@wikingagresor]

The best 'mindfuck' in complex nuber is: i ^ 2 = -1

[@pinocleen]

I do Cornflakes numbers every morning.

[@RPBCACUEAIIBH]

7:36 So if you've got a real value and change the phase angle by 90° you get the BS value. Got it! :D

[@dinodubroja7433]

Isnt RMS (root mean square) an effective value of waveform (square root of two times samller then peak-for sine wave only), you said its peak at the begging just wanted to meantion so people dont get confused (cca 1:50)

[@ignispurgatorius5297]

Nice video about the fundamentals of AC calculations. But I'd argue polar and rectangular conversion has lost alot of meaning today when your average scientific/school calculator can calculate complex numbers natively and you can just punch in the complex multiplication/division as is. In the cases where you aren't allowed to use a calculator (and those still exist in some courses), the difference between doing a division by extension with konjugated complex numbers isn't that much harder either since you need to solve a pythagoras for polar conversion as well, not to mention the arc function. Complex multiplaction is trivial anyway and a good idea to learn as a principle for vector calculus should you make it to up to field and wave theory in 3d spaces (paraphrasing, because I have no idea what it's called in English). Essentially you only get something out of it if you are only allowed to use an old scientific calaculator, which even during my time in uni 10 years ago was already becoming exceptionally rare. Either we weren't allowed to use a calculator at all, we were allowed to use a 4 banger or we could go all out with a scientific calculator (sometimes with a clause that it may not be capable of graphics and non-programable). By the way, I just noticed my stupid smartphone calculator doesn't even have polar rectangular conversion, at least I can't figure out where it may be. Weird choice to have hyperbolic functions but not simple conversions like that. PS: Also you drew a -5+j4 there. ;)

[@cammedred8624]

👍

[@evensgrey]

6:00 You use j for the imaginary component instead of i because i is already spoken for as current (at least, when you get into the field theory part of things that comes up in some extreme circuit design). Now, why complex numbers, when there are other representations of vectors that add the same way? Because those methods don't MULTIPLY the way currents, voltages, and impedances do, but complex numbers do. In spatial vector systems, when you multiply two vectors you either get a scalar (no direction) or a vector at right angles to the two original angles, rather than just another complex number. (Imaginary is an arbitrary designation, chosen in contrast to the Real Numbers that the Imaginary Numbers are at right angles to. One interesting feature of all complex number systems, of which there are infinitely many, is they all require you to give up some obvious, simple property that Real Numbers have. The simplest set, the Complex Plain, forces you to give up all numbers being in a single magnitude ordering.)

[@darranrowe174]

From what I remember, while there may be infinitely many complex number systems, only the 2 dimensional one works.

[@Rene_Christensen]

At 19:55 the reactance is not correct, as j should be removed. The imaginary part is jX, so X is real.