Proof of Euler's Formula Without Taylor Series (Most Beautiful Equation in Math)

Jesus Christ is NOT white. Jesus Christ CANNOT be white, it is a matter of biblical evidence. Jesus said don't image worship. Beyond this, images of white Jesus are not just blasphemous and criminal, white Jesus is from Satan ( the imposter.) Why? Let's look at what Satan does:
1) He is incredibly narcissistic and promotes himself shamelessly.
2) He misleads and confuses.
3) He pushes people away from Jesus Christ God, the Holy Trinity, the one and only messiah. White Jesus does all three of the above and more -- matching the ways of Satan.

Statues of Christ are equally offensive to God the Christ. While money is the biggest idol, Jesus spoke sufficiently against carved images.
--------------------------------------------------------------------------------------------------------------------------------------------------------------

You can also find me on Tik Tok @reuslovesmath and @polarpiny

[billeast]

Thank you, thank you, thank you! I have spent too much time looking for this. There is one on wikipedia similar to this, but they just skip through a lot of the explanation and say that proves everything. This should replace that.

[AlexLi]

Key word is complex number in polar form which establishes relations between trig and exp functions. Great work. Thanks.

[hamzasaeedmalik]

Hey I know I'm commenting again but really thankyou for helping me out this is the most amazing stuff I found regarding euler's equation, thankyou polarpi

[xiaoshen]

Hey christian soul, love from. a hindu soul!! 😍

[cebiclock]

great video! The proof seems pretty simple, which makes me wonder: are we using something that Euler couldn't have used? i mean where's the trick hahaha

[constantine]

This is a math trick…not the proof to visualise the Euler identity

[Shubham_pandey-nkun]

It was really cool.
Great video dude.

[MrDiamondShoes]

You sound like Chris from Family guy (no offense)

[Dai-Verse-IT]

Remember this years ago and it showed me how elegant mathematics can be.

[Salmanul_]

This equation is really beautiful and also very useful.

[prabeshbashyal]

What is your name? I really loved the voice.❤

[naziyapappuwale]

I m from India still i understand your language thank you nice explanation ✨

[quintonrice]

If theta does not equal zero, can you still show that k = 1. I know it will because the function is a constant for all theta, however, just as an exercise if you pick any other theta value, how can you show that it k = 1? Try, for example theta = pi/2. How would you prove that k = 1 in that case, without Euler's formula?

[jyothinkjayan]

How can we generalise by taki g theta =0, instead if we take some anither number then last equation's multiplicative term changes

[herbie_the_hillbillie_goat]

Very nice proof. It seems very "Eulerian".😁 Just wondering, did you come up with it?

[bernhardriemann]

why would someone even consider that function i.e f(x)= e^(-ix) {cos(x)+isin(x)}, where does this function show up in nature or maths? and also loved the proof.

[pavelgatnar]

It's overcomplicated.
Let f(x) = cos(x) + i*sin(x)
f'(x) = -sin(x) + i*cos(x) = i*(i*sin(x) + cos(x))
So f'(x) = i*f(x), f(0)=1 => f(x) = e^(i*x).