i^i
1,251,004
Published 2017-07-25
This is a classic complex numbers question and in fact i^i is real!
How about i^i^i? Check this out: • tetration of i^i^i = ?
Are you wondering about (a+bi)^(c+di) now? Here's the video • the tetration of (1+i) and the (a+bi)...
#blackpenredpen #math #complexnumbers
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All Comments (20)
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I'm watching this instead of doing math homework.
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Euler had a hard time understanding negative numbers, but with complex numbers he is just fine.
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0:03 My friends when I talk about mathmatics
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me: i is complex my English teacher: no "i AM complex"
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Another simple way to get the same result: We know that: e^iπ = - 1 (e^iπ)^1/2 = (-1)^1/2 e^i(π/2) = i So if we raise to the i power we get: e^(-π/2) = i^i :)
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blackshirtredshirt :D
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This absolute madlad pulled out another blackboard from the ceiling. Most badass thing I've ever seen on a math class
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Hey I just watched this video yesterday and it came in my mathematics exam today Nobody but me solved it
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Hey man I love your videos, the way you explain the problems and also how much you enjoy it all! Keep up the great work!
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"5" is a complex number: a knuckle sandwich is lunch.
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I am just getting addicted to this channel
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I like the back stories you provide, and your logic and steps are very easy to follow!! Please keep this channel alive, watch it every day! It’s great for my engineering students too.
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6:50: 'You know this is a real number. So real." XD
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"Hopefully this makes everybody happy." (10:04) This is the internet! It is mathematically impossible to make everybody happy.
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Another very similar way to get to the same result, but without using ln: i^i = ? But, i = 0 + 1i = cos(t) + sin(t)i t = pi/2 (or pi/2 + 2*pi*k) solves the equation. So, i = e^it i = e^(i*pi/2) i^i = [e^(i*pi/2)]^i i^i = e^[(i^2)*pi/2] i^i = e^(-pi/2)
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I really enjoy the efforts you make in complex algebra calculations. Many people get beat down with endless calculation but few ever tell them there are calculations that no human can do, so don’t get discouraged. Just increase your focus and attention span over time. I’ve had professors who would assign us twenty 3x3 matrix inverse problems to be done by next week, but couldn’t do one on the board without making ten arithmetic mistakes.
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I have no idea why some people dislike your videos. Honestly, the work you do is amazing. It's very understandable and really nice! Thank you so much!
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The nice thing about your videos is that they are very calm and relaxing. And your enthusiasm cancels out the boredom :D
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If I've learned anything, it's always have a pokeball ready. Just in case.
