The imaginary number i is equal to the square root of negative 1. But i^i is a real number, approximately equal to 0.208. Why is this true? It is an incredibly tricky calculation if you want to justify the steps properly. All of the videos I've seen on i^i use an unjustified step, including mine. So what is the proper way to calculate i to the power of i? Special thanks this month to: Daniel Lewis, Kyle, Lee Redden, Mike Robertson. Thanks to all supporters on Patreon!   / mindyourdecisions  

0:00 calculation
2:11 complex numbers
3:30 "proof" 1
6:21 "proof" 2
8:20 complex exp
9:12 complex log
12:32 the right way

WolframAlpha
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Math StackExchange
https://math.stackexchange.com/questi...
https://math.stackexchange.com/questi...
https://math.stackexchange.com/questi...
https://math.stackexchange.com/questi...
https://en.wikipedia.org/wiki/Princip...
Complex Variables and Applications, James Ward Brown, Ruel V. Churchill, 7th edition, Chapter 1 Section 8, Roots of Complex Numbers
The complex logarithm, exponential and power functions, Professor Howard Haber
https://scipp.ucsc.edu/~haber/ph116A/...

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