DeMoivre's Theorem Induction Proof: (cos(x) + isin(x))^n = cos(nx) + isin(nx)
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- เผยแพร่เมื่อ 8 ต.ค. 2024
- In this video I prove DeMoivre's Theorem using the principal of mathematical induction. This is also called DeMoivre's Formula or DeMoivre's Identity. This is a fun proof. I hope this helps someone.
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Thank you:)
I love videos like this. Clear handwriting, none writing on black screen in which some colours get lost as in the eyes of colour-blind or night blind.
👍
Another great video! These hand written proofs are really nice to follow along. Thank you!
Please, don’t stop making these. Please!
problems that involve solving for complex roots is my personal favourite ... demoivre's thm is very helpful in this case and is a great thm to demo induction.
Wouldn't it be easier just to use Euler's fórmula?:
(cos(a)+isin(a))^n=e^(n•a•i)=cos(na)+isin(na)
(e^(a•i))^n = (e^(n•a•i)) for a real number a is only true when n is an integer, which is what is being proven in the video.
Love videos like this,
Please do more like this…
You inspire me alot…
Could you do another induction proof via the strong induction?
Yes I will try to do some of those soon! Thank you!!
iirc, this theorem gets an extensive workout in the Advanced Engineering books.
Yes!
What is first Euler or Moivre Formulas?. In high school math they teach Moivre but they do not give Euler's. It seems to me that they are same. In fact you can reach Euler's formula from Moivre's by making a 'definition'.
Can't we just use the Taylor expansion of cos and sin?
Although I must say I like this explanation, it's more elegant.
Would this be a good textbook to learn about proofs?
Yeah I think it's pretty good:) There are other good ones too. I also like this one a lot
th-cam.com/video/qnyivxMBsqU/w-d-xo.html
@@TheMathSorcerer have you taken a look at “How to prove it: A structured approach” by Velleman? If not, I highly recommend it! Especially the newest edition since it has great introductory chapters to number theory and algebra. It’s great for both beginners and the experienced. However, you can’t really beat the “what’s wrong with this proof?” Type questions from “Transition to Advanced Mathematics”.
I just got the Velleman book but I think it’s an older edition. I will look at it soon and maybe work through some problems! It’s exciting thank you!
How do you proof it for complex numbers?
lol