There is no "i" in the exponent. Wolframalpha says it is single-valued. Why is this? And why is i^i^i^i multi-valued but i^i^i single valued? Maybe wolframalpha is wrong?
The infinite power tower i^i^i^i... has a fixed point. I spent a couple of minutes this afternoon working it out. Now you've done several videos on the Lambert W function this could be another one.
swiss knight Because we are saying i^(i^i), not (i^i)^i. These are completely different. For example, what is 3^(2^3)? That would be 3^8 = 6561. If I changed it to (3^2)^3, we get 9^3 = 729. When we don’t include parentheses, we assume the former, not the latter; therefore, you cannot simply multiply the exponents.
@@camdamcool6125 Correct me if I am wrong, but I think that's not quite the answer. Common interpretation of i^i^i^i is i^(i^(i^i))), while (e^-pi/2)^(e^-pi/2) is (i^i)^(i^i).
Dear mr BlackpenRedpen I have a question for you. One of my favourite graphs is (X^2 + 2x -8)^2 + (y^2 +2y -8)^2 = 81 I wondered if it is possible to find the area that is enclosed by this graph (it’s shape is two diagonally overlapping ovals). I am not aware of any rules that make it impossible to calculate this so I would appreciate if you would reply or maybe do a video on it :)
Did I make it?
blackpenredpen yes good job
Sonic the hedgehog is impressed : D
blackpenredpen barely, well done
We want to explain the million dollar problems, the Clay Institute, can you?
Your videos raise my mood so much, even when I'm already happy. It's wonderful to see someone appreciate the beauty of mathematics that much!
Next week: 61 seconds in ONE minute.
Your comment has 61 likes! (I'm not one of them, unfortunately)
@@pronounjow and now it has 69 lol!
And now it doesn't... 420, here we come!
I want to like this comment but it has 420 sooooo....
Next week: π is irrational (1min uncut)
Next week: π is transcendental (1min uncut)
Next week: Poincare conjecture in 1 min(uncut)
Next week: proving the Riemann hypothesis (1 min uncut)
Next week: proving the Collatz Conjecture (1 min uncut)
Next comment:something about Fermat last theorem and how the proof is too short for a 1 minute video...blablabla
The way he just cut himself at the end
Da E
I didn’t cut the video. I pressed the stop button on my laptop.
@@blackpenredpen
😂😂
You're deriving so fast you could get speeding ticket.
😂😂😂😂
Lmao. And he's switching colors too, which makes it more impressive
Lmao best one so far
Did this inspire the Lambertghini?
As long as he doesn't drink and derive it's perfectly legal.
Sonic: I am speed
blackpenredpen: Hold my pen
There too many they keep falling off Sonic's hand 😂
BlackpenBluepenRedpen and legendary purple pen
Or in this case: "Give me my markers".
the red one or the black?
The marker switching is on point today 👌
Oracle thanks!!! And I stay true to black pen red pen
One thing I love about you is how genuine you are. Never change !
Thank you!! : )
Not only did he solve it under 1 minute, he switched pens while doing that.
Teacher: you have one minute to finish the exam
Me:
Hahaha
😂😂
Did I make it?
wtf did just happend
quick maffs
Crossover:
100 integrals in 1 minute?
Physically impossible. But 1 hour would be interesting
@@Aditya_V_R it was a joke boomer
Nicola Barbaro that doesn’t even make sense
@@markq722 ok boomer
@Popa Ionut ok boomer
General solution:
i^i^i = e^[(2m+1/2)π * (e^(2n-1/2)π)]
Where {m, n}∈Z
Okay, I know, sprint run right? Then let m=n=1.
There is no "i" in the exponent.
Wolframalpha says it is single-valued. Why is this? And why is i^i^i^i multi-valued but i^i^i single valued? Maybe wolframalpha is wrong?
The infinite power tower i^i^i^i... has a fixed point. I spent a couple of minutes this afternoon working it out. Now you've done several videos on the Lambert W function this could be another one.
@@bulletprooftrading what
@@bulletprooftrading i don't think that would be obvious to everyone.
@@sylviaxx3574 Yes, most folk are oblivious! to such fun stuff. ;-)
Yes, you did!
Incredible job, BPRP!
Love ur videos)
FrozenArtStudio thank you!!!
The proof of Fermat's Last Theorem in 1 minute.
I have a most elegant proof that can be explained in under 1 minute.
But this comment box is too small to contain it.
@@SuperYtc1
Ah, the true spirit of Fermat.
We want more 1 minute challenge
We love it
I love these 1 minute explanations even though I usually have no idea what he says at the end
love your 1m chalange
Please do i^i^i^i^i^i^... (infinite cascade) in one minute!
He even switches the pens
Exynouz : ) yea
Next: Solving String theory in pi minutes.
+1
😏Yeah but we can make it 30 sec by keeping playback speed 2x.
Protip!
The way he stopped the recording at the end to see if he could make it or not😂😂. Really appreciate it, it must jad took several re-attempts!
I just watched this video in x2 and I have travelled to the past.
THIS MAN GOING LIGHT SPEED
Just the speed of the sound at the moment and thanks!!
Bruh wtf I thought my playback speed was 2x when the video started 💀
2021:
"proving N=PN speedrun"
what a result at end !!! amazing what we can do in complex numbers
“No one can possibly solve this in a minute.”
BPRP: 🙋🏾♂️
This is why I like math. You can flex on people with very fast minecraft enchanting symbols.
blackpenredpen 一位用生命拍片的RUclipsr
Kobe Cheung wow what a comment!!
This is clearly just a slanted -i.
Well done
Why isn't it 1/i?
Because i^i^i = i^i*i = i^(-1) = 1/i
Right?
(1/i = i/-1= -i)
swiss knight Because we are saying i^(i^i), not (i^i)^i.
These are completely different. For example, what is 3^(2^3)? That would be 3^8 = 6561. If I changed it to (3^2)^3, we get 9^3 = 729. When we don’t include parentheses, we assume the former, not the latter; therefore, you cannot simply multiply the exponents.
@@FACH-nr3jz thank you kind stranger
Lowkey this actually made sense to me
You made it alright!
In other simple words (i^i)^i = -i
Eminem: im the fastest rapper!
BPRP: *hold my pens*
blackpenredpen make a vid on, find the coordinates of the intersection between y=sin(1/x^x) and y=cos(1/x^x) pls.
We can also use logarithm for more simplification🌟🌟
best minute spent today
BRAVO, SIR!!!! :) :)
What about i^i^ (infinite times?)
Does it will have solution?
I want i^i^i^i in 1 minute next time!!!
Just write it as i^x, where x is i^i, and express it like e^(ln(i^x))=e^(i^i ln(i)), since we know what i^i and ln(i) are, the rest is easy peasy.
AMAZING 😚😀
that was quick
Thanks Euler
Usain bolt : i am the fastest man alive
Blackpenredpen : hold my pen ... wait, how am i suppose to write on board ?.
Why didn't you raise i^i = e^(-pi/2) to the i-th power, just multiply the powers? You would get e^i(-pi/2) = -i
Elx_Dude Because a^b^c=a^(b^c), not (a^b)^c.
Could you also have done (i^i)^i?
Would haven been e^-pi/2e^ipi/2
YAY! GOOD JOB may you please explain the integral of ln(i+x)?
This is content I subbed for
That’s quite straightforward once you write (exp(a))^b=exp(ab).
Great Job!!
Wow nice timing
OMG that was impressive :>
LOVED it. Laughing out loud, AWESOME! :)
Blackinem - Math god
The pace on this lad
i just know that you were originally gonna not do the principal value initially, but then you decided you had to in order to save time
For the next video, you should try to evaluate or take the derivative of i↑↑i.
1. That's not a function of x, so you can't differentiate it.
2. The mathematics to evaluate that hasn't been invented yet.
@@oledakaajel oh :(
I was also going to say differentiate x↑↑x but you're right. The math hasn't been invented yet.
That ending tho :D Well done blackpenredpen
LOL, next up i^i^i^i in 1 minute!
Just (e^-pi/2)^(e^-pi/2) lol
@@camdamcool6125 Correct me if I am wrong, but I think that's not quite the answer. Common interpretation of i^i^i^i is i^(i^(i^i))), while (e^-pi/2)^(e^-pi/2) is (i^i)^(i^i).
integral (sinx)^2/(x^2) from 0 to infinity
I love this
Next: Twin prime conjecture in under one minute
1 second left! Impressive!
why do you use the big ball shaped mic? wouldn't it be easier to buy a mic that clips on to your shirt so you have 2 hands?
RIP blue pen
😭😭the blue pen died in the making of this video
Bprp: 1 minute
RUclips: 1:01
That was an intense sports
20 seconds in my head is hurting
famous last words: did I make it
=0.947158991 + i(0.32076445), in case you wanted to know the values
I love you, dude... the great solution and also you made me laugh)))))))))))
I think this was unlisted, but why. And you did it 👌👍
Dear mr BlackpenRedpen I have a question for you.
One of my favourite graphs is (X^2 + 2x -8)^2 + (y^2 +2y -8)^2 = 81
I wondered if it is possible to find the area that is enclosed by this graph (it’s shape is two diagonally overlapping ovals). I am not aware of any rules that make it impossible to calculate this so I would appreciate if you would reply or maybe do a video on it :)
You did this like I did my group theory homework yesterday
I sent the work 21 seconds before the deadline
Next video: Holding a microphone for 100 hours nonstop while doing math
and now the standard model of the particle physics in one minute
That was fast
Next week: i^i^i^i^i^i^i^i.... 1min uncut
Next week:
Proving Riemann hypothesis (1 min)
Maths make people crazy
Could be i^i^i=-i?
Bloody fast
Good job
Brain.Exe stopped working
Next week: the history of the entire world in one minute
Me on the ap calc exam with one minute left and everythings coming back to me
New challenge: i^i^i^i (just kidding, this probably will take another minute to have a result)
Nah he can just say "I've done a video on i^i^i".
Plz explain calculus 3 section 16,15
That handwriting at the end though.
Amazing 👏👏👏👏👏
Please, plot the series a(1)=i, a(n+1)=a(n)^i in the complex plane.
you should do "proving that p=np (1 minute uncut)"
next week: sin(x)^cos(x) = 2 in one minute
i to the i to the i in |i| minute.