Question

Genius Question: Why is i^i^i^i^i^i^e = 1
where i = sqrt(-1)

Answer 1

http://www.wolframalpha.com/input/?i=i^i^i^i^i^i^e

Answer 2

please show why this is equal to 1, you can use exponential polar form, for example
i = exp(pi/2*i)

Answer 3

Look at
\[\large
2^{(3^4)}=2417851639229258349412352\\

(2^ 3)^4=4096
\]
Where are your parentheses in your question?

Answer 4

yes i know that

Answer 5

i^i^i^i^i^i^e =i^(i^(i^(i^(i^(i^e))))

Answer 6

exponentiation is right associative

Answer 7

i^i^i^i^i^i^e = 1
take ln for both
e ln i^i^i^i^i^i =0
so ln i^i^i^i^i^i =0
then must be i^i^i^i^i^i =1
take ln
i ln i^i^i^i^i =0
i^i^i^i^i =1
ln again
i ln i^i^i^i =0
i^i^i^i =1
ln also
i ln i^i^i =0
i^i^i =1
ln again
i ln i^i =0
i^i =1
i ln i =0
i=1 its a contradiction so im not sure there is somthing wrong i think in my answer

Answer 8

let me check that over, it looks wrong

Answer 9

you took ln of both sides