Informal Proof of Euler's Formula (1 of 2: Exponential calculus)

[@kiaruna]

Having him as a teacher is a blessing, I hope his students realize they're the luckiest in the world

[@jeremypnet]

I've been waiting for this bit since he started on complex numbers. Euler's formula is my favourite equation.

[@GreatMollyHatchet]

I remember learning about Euler's formula in Calc 2 in college and it blew my mind. To see the 5 most used constants in mathematics related to each other in one clean equation is insane.

[@unknowngirl417]

Sir , I am from India and you are my favourite teacher.

[@colinyvergniaux8156]

As a french student I find your explanation super clean so thanks you a lot

[@idjles]

3:18 only in Australia can you sneeze in class in 2021 and no one notices.

[@idjles]

Only in Australia can you get a cold in winter in 2021. In Europe no one caught a cold in winter - no one is buying cough medicine from the pharmacy.

[@DrSivaMahalingam]

I wish I had this guy as a teacher in highschool. What a legend.

[@alessandrocaia1270]

I really can't wait for the second part

[@kaarunyamummoorthi7580]

started this topic as a chore but rn.. I AM TOTALLY INVESTED

[@tadejsivic534]

Yes! Can't wait for the grand finale, to connect polar form, trigonometry, e and i and pi and... just a beautiful equation.

[@ambroselam626]

I don’t like cliffhangers but I like the fact that I know where this is going :)

[@habibaamir8830]

thanks for this cool video

[@oliverqueen5883]

What year group is this?

[@just7815]

15:18 probably not

[@playdoh1975]

when I took calculus we didn't say (a) dash.... we said (a) prime... wonder if this is an Australian way of expressing derivatives....

[@MCLooyverse]

It's just a different name for the apostrophe/prime/dash. Same symbol though.

[@artliil5687]

What grade?

[@musicsubicandcebu1774]

cos A + cos B = cos(A+B)? what am I missing?

[@EpiCuber7]

Or rather, (cosA+isinA)*(cosB+isinB) happens to have a real component cos(A+B). This is because the arguments are added when two complex numbers are multiplied.

[@musicsubicandcebu1774]

@@EpiCuber7 Thanks for that

[@MCLooyverse]

@@EpiCuber7 That's not the reasoning they're using. They expand it out: (cos(α) + i sin(α))(cos(β) + i sin(β)) = (cos(α)cos(β) - sin(α)sin(β)) + i(cos(α)sin(β) + cos(β)sin(α)) = (if you happen to know your trig identities:) cos(α + β) + i sin(α + β) I do not know my trig identities, so I always have to do this process backwards ("Wait, what's cos(α + β)? *sigh* e^(i(α + β)) = e^(iα) * e^(iβ) = ... *mumble mumble mumble*")

[@mathsmakhan5605]

Cos(A+B)=(CosA×CosB) + (SinA×SinB)

[@EpiCuber7]

@@mathsmakhan5605 -*

[@PauxloE]

Writing e = 1.718281828... "and it keeps going" is kind of evil (it suggest that the 1828 are repeated digits, i.e. e is rational).

[@marvn1224]

Why tf my teachers do not explain same as this teacher !!!!!!!!!!!!!!

[@tg509]

There are many ways of introducing this topic. When I studied it at A level, we'd already covered Taylor and Maclaurin series so we started with the Maclaurin series of e^x, cos(x) and sin(x).

[@tarekhany9856]

Why didn't we apply the chain rule on deferentiating ib(x)?

[@brd8764]

SA

[@pelasgeuspelasgeus4634]

"Exotic" he said! The square root of a negative number! I call it fake invented math.

[@AndresFirte]

How is it fake?

[@brd8764]

s....