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.
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.
@@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*")
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).
Having him as a teacher is a blessing, I hope his students realize they're the luckiest in the world
I've been waiting for this bit since he started on complex numbers. Euler's formula is my favourite equation.
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.
Sir , I am from India and you are my favourite teacher.
I really can't wait for the second part
3:18 only in Australia can you sneeze in class in 2021 and no one notices.
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.
As a french student I find your explanation super clean so thanks you a lot
I wish I had this guy as a teacher in highschool. What a legend.
Yes! Can't wait for the grand finale, to connect polar form, trigonometry, e and i and pi and... just a beautiful equation.
started this topic as a chore but rn.. I AM TOTALLY INVESTED
thanks for this cool video
I don’t like cliffhangers but I like the fact that I know where this is going :)
What year group is this?
What grade?
when I took calculus we didn't say (a) dash.... we said (a) prime... wonder if this is an Australian way of expressing derivatives....
It's just a different name for the apostrophe/prime/dash. Same symbol though.
15:18 probably not
Why didn't we apply the chain rule on deferentiating ib(x)?
cos A + cos B = cos(A+B)? what am I missing?
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.
@@EpiCuber7 Thanks for that
@@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*")
Cos(A+B)=(CosA×CosB) + (SinA×SinB)
@@mathsmakhan5605 -*
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).
SA
Why tf my teachers do not explain same as this teacher !!!!!!!!!!!!!!
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).
s....
"Exotic" he said! The square root of a negative number! I call it fake invented math.
How is it fake?