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@EclecticSceptic Hi, sorry it didn't work for you! Analogies are personal -- for me, I see the equation as relating linear motion (sine + cosine) to rotation (move out, and rotate up).

betterexplained 5 months ago

quote : as a rotational and oscillatory operator. you should make additional videos from your book--you have great perspective .

Colin , yes plz make more videos about the above , rotational and oscillatory operator , for people who dont have money to buy your ebook and wanna learn this electronics math stuff , lots out there .

But I just bought your Ebook , I like your nice clear images .

dankiewfc 7 months ago

hi--i really liked your book--but if feel like this is very non-intuitive. i think its much easier to set it up by showing how eulers formula appears in converting to the polar form of complex numbers. So e^i is intrinsically rotational. The growth in a circle is interesting--but obscures e as a rotational and oscillatory operator. you should make additional videos from your book--you have great perspective

anzatzi 8 months ago

@anzatzi Thanks for the note! Yes, there's a few ways to tackle e -- as you say, e^i has rotation built in. I might be confused about your comment -- I think growth following the path of a circle is basically a rotation right? However, there might be another way to state it which gets the point across more clearly too. I'd definitely like to make some more videos from the book :)

betterexplained 7 months ago

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anzatzi 8 months ago

Can you answer this for me:

6÷2(1+2)

bemyescape84 10 months ago

Wonderful explanation, thank you!

ProsperosCloset 10 months ago

I have a question, how can one define "i" as e^(i*pi/2). I didn't think you could define something with that something. Or, correct me if I'm wrong. Good video.

Padenormous 11 months ago

@Padenormous Yeah, I don't see it as much as a "definition" and more as showing another way to get to i. It's a bit like saying 4/2 = 2... yes, you used 2 in the explanation of itself, but the idea is to say "You can see 2 on its own, or as half of 4." Similarly, you can see i as a single rotation on its own (just straight "i"), or the result of taking "1" and rotating it upwards 90 degrees (e^i * pi/2).

betterexplained 10 months ago

This formula was in a book I read recently "The Housekeeper and the Professor". I highly recommend it. Your video was the only one I could find that I a layman could understand. Btw, the audio is too low, I had it maxed out. I think you would be a good teacher. Thanks for the video.

igottaknow 11 months ago

I've got a wonderful idea. Why not write this up with excellent graphics, then page through it too fast for anyone to read it.

gamesbok 11 months ago

@gamesbok This was more of a walkthrough, not really meant to be read. The full article is in the description, hope that helps.

betterexplained 10 months ago

Wow my Algebra teacher sucks. Couldn't explain in 3 classes what you just explained in 10 minutes. Thank you so much!

TheCancunBaby 11 months ago

@TheCancunBaby Thank you!

betterexplained 10 months ago

I've been to a lot of math lectures with many experienced professors. This young man has done an amazing presentation. The best 10 minutes on an academic topic I have ever witnessed.

dwightivany 1 year ago 4

@dwightivany Wow, thank you for that message! It's so encouraging to hear that it's helpful -- I hope to make many more like this.

betterexplained 1 year ago

@dwightivany Thanks for the kind words!

betterexplained 10 months ago

great vid!

f20081985 1 year ago

you know, you can also use his equation to prove that cos(i)+i*sin(i)=1/e

TheMikeSideGallery 1 year ago

Very lucid.

EdMahoney19 1 year ago

Imaginary Numbers - Breakthrough

/watch?v=MO5LgzTsI58

fonsidream 1 year ago

Thanks for your prompt reply Kalid. It's a pity it doesn't run on Windows and not exactly free, otherwise I might have tried it on VirtualBox.

consultjohan 1 year ago

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consultjohan 1 year ago

Kalid, How did you make this video and what software did you use? I like the way you put yourself in the corner, and at the same time explain with the cursor on the screen--just like in a lecture room!

consultjohan 1 year ago

@consultjohan I used ScreenFlow on Mac -- it makes it easy to both capture and combine your screen and webcam. Yeah, I like having a way to show gestures, etc. vs. just your voice.

betterexplained 1 year ago

i ve been following your blog for a while and very glad to see a screen cast :)

Its much easier and fun to watch a video before starting on text.

I have come across Benjamins quote on Eulers equation, and took his quote for granted and never made an attempt to understand the equation. Once you have explained all the components of the equation, it doesn't seem to be a mystery anymore !

Excellent work :) subscribing right away .

supergopi 1 year ago

@supergopi Thanks -- yes, that quote really struck a nerve with me because I had resigned myself to not understanding the formula when I first encoutered it also. Appreciate the support :)

betterexplained 1 year ago

I totally love seeing the screen-cast! (sorry, i am behind in my better explained subscription) This is a great explanation!

MrTheSuperHead 1 year ago

@MrTheSuperHead Awesome, thanks! I plan on doing this for more articles.

betterexplained 1 year ago

I'm a chemist and have had my fair share of math and physics courses where this has been relevant, but it has never made as much intuitive sense (as a whole or the individual parts like raising to the power of i) as it does now! Time to go check out your other stuff!

lankyjuggler 1 year ago

@lankyjuggler Thanks, hope you enjoy it! As a chemist you may enjoy the articles on ln and e, as they seem to appear in a ton of chem formulas :). It took a while before I could start to see them intuitively.

betterexplained 1 year ago