Intuition for i to the power i | Lockdown math ep. 9

2020-05-15

[public] 295K views, 9.39K likes, 108 dislikes audio only

i^i, visualized and explained.

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Mistakes:

At 1:06:20, when changing r to equal 0.69*i, I said "this is what we might think of as (2i)^x", but that is not correct. It's what we'd think of as [Exp(ln(2)*i)]^x for whatever complex number Exp(ln(2)*i) is.

Beautiful notes by Ngân Vũ

https://twitter.com/ThuyNganVu/status/1263522876403011585

Video by Matt Parker:

/youtube/video/9tlHQOKMHGA

Video by Red Pen Black Pen

https://youtu.be/ABk1HK2AR2E

Thanks to these viewers for their contributions to translations

Hebrew: Omer Tuchfeld

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Video timeline (thanks to user "nooonesperfect")

0:18 Exponential function for i^i

1:26 Question 1

2:27 Plug-in imaginary number in exp(x) polynomial

3:38 Answer 1 and explanation

7:35 What it really means i^i?

9:14 e^it as a position vector

11:30 Question 2

12:39 Audience question from twitter

13:14 Answer 2

14:52 Where you get after traveling π/2 units of time for position vector e^it

19:48 Question 3

20:42 Audience tweets

23:34 Answer 3

35:50 Question 4

37:11 Answer 4

40:11 How exp(rx) or b^x really works?

46:28 Question 5

47:49 Audience tweets

49:26 Answer 5

57:06 Visualization of f(x)= exp(r*x) i.e. e^(r*x), where r= unique complex number

1:06:06 Questions to think about

1:08:51 Audience tweets

1:09:09 Power tower for i

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