Euler's Formula Proof

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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

[reecejo]

Not only does the identity contain the 5 most important constants in all of mathematics, but it also has the 3 fundamental operations of arithmetic, addition, multiplication, and raising to a power, and it has the singular concept of equality. 5, 3, 1 -- the beauty and elegance are awe-inspiring.

[prasoonpandey]

Thanks a lot! I was amazed how cos x + isin x could equal e^ix but you made it look so simple.

[surajthakkar]

Thank you so much. You are doing a wonderful job. I was very confused about this but you made it neat and simple. Thank you man keep posting such videos.

[drgaryrobertshaw]

Explained simply and very clearly. Excellent.

[johnnolen]

There's an easier way to prove Euler's formula. Consider z = e^(ix), then dz/dx = i*e^(ix) --> dz/dx = i*z. Now consider, w = cos x + i sinx. dw/dx = -sinx + i cosx = i*(cosx + i sinx) --> dw/dx = i*w. Any two functions that obey the same differential equation are equivalent to one another. Thus z = w. QED.

[shashankjha]

Till now, from all the proofs that I've come across, this one is on another league.

[real_orestis_georgiou]

Incredible! A very simple and understandable proof, using only the Taylor series.

[jeffreyluciana]

I bet Euler had a few tankards of ale when he discovered his famous equation

[janardanchavan]

Sir! Thanks for geometry videos but upload furthur concepts of it. I am waiting for your videos eagerly. Also suggest some book for geometry as i suggested you i you have read the comments of previous videos. Plz reply! Upload soon.

[celk]

I’ve felt the passion of math genius. Nice job

[titelmund]

Could you just explain why it is ok to rearrange and regroup terms in an infinite series?

[riemanngeometry]

Nice video, but can you explain why e^x is equal to If you can, that will be pleasure for me

[SaurabhSingh-vvsr]

this isn't made by euler, the real euler identity is π²/6=1⁻²+2⁻²+3⁻²+4⁻²+5⁻²+...
However good video.

[n.l.]

Is it possible to factor Euler’s Formula like some quadratic equations? Factor e^(i*pi) + 1 = 0 into the form of (px +r)(qx + s) = 0?