Harvard Entrance Exam Question | Can you solve?
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- เผยแพร่เมื่อ 16 ธ.ค. 2024
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your answer is one of the infinitely-many values. this is because -1 = exp[i*(pi + 2*pi*n)] where n = ...,-2,-1,0,1,2,...
therefore, the final answer is exp[i*pi^3/2 (1+2*n)] where n = ...,-2,-1,0,1,2,...
You need to write the pi symbol more clearly as it often appears as though you are writing the variable x!
Okay 👍
Too slow in writing.😂
Yeah
The exponents are in the way that can't be written fast...and it may cause any missunderstanding.
You can watch it on 2x speed🤗
hold down left click, very useful
It's tedious to write the same expression over and over again.
@@xbia1 I agree, it breaks the flow.
(x ➖ 1pix+1pi).
-3 y. Course y -1 √>>t =202
D
A questão é interessante, mas é preciso especificar melhor até que ponto deve- se resolvê-la. BRASIL Dezembro de 2024.
Alright Boss 😊
Thanks for sharing your precious feedback 😌
Could have gone straight from 2:52 to 4:46 without losing anyone.
😂😂😂
cos(π^3/2) + sin(π^3/2)*i ~= (0.7551868,-0.6555097) (together with all z that differ by 2π in the argument)
Euler formula is simply wrong. One side is the exp function which tends to infinity and the other side is a sum of 2 trig functions each ranging from -1 to 1, ie it's finite. So, these 2 sides can't be equal.
Euler's equation is well established. When the exponent of e is purely imaginary as it is here, the result has a magnitude of 1, and simply spins around the origin in the complex plane, not tending to infinity. Complex numbers are weird and unintuitive. Imaginary exponents are tough to wrap your head around.
@immovableobjectify Euler formula was derived by setting iθ in the exponent Taylor series. Right? But that exp series was validated for real numbers, not for imaginary numbers. So, using it to derive the formula was simply erroneous. And I described why it is erroneous. Try to understand it.