08/07/2011, 11:17 PM
(This post was last modified: 06/27/2022, 07:51 AM by Gottfried.

*Edit Reason: Put the formula in better readable Mathjax*)
What is the Fibonacci root of i, or to put it another way, what is the equation of x when

\( \Large \quad \quad {({1+\sqrt 5\over 2})^x-(-1)^x ( { 2\over 1+\sqrt 5})^x \over \sqrt 5}=n \)

?

All I need is a formular and I am capable of just entering the eqution and i straight into Google calculator to get a result.

I'm interested as decimal numbers entered into the Fibonacci function manly get complex results which shows a link between the function and i, and suggests that the Fibonacci root of i might not be complex and might be of some importance.

I know this isn't really to do with Tetration, but I've asked this across the internet and have not have any replies and I'll be greatfull for any help.

Thanks.

\( \Large \quad \quad {({1+\sqrt 5\over 2})^x-(-1)^x ( { 2\over 1+\sqrt 5})^x \over \sqrt 5}=n \)

?

All I need is a formular and I am capable of just entering the eqution and i straight into Google calculator to get a result.

I'm interested as decimal numbers entered into the Fibonacci function manly get complex results which shows a link between the function and i, and suggests that the Fibonacci root of i might not be complex and might be of some importance.

I know this isn't really to do with Tetration, but I've asked this across the internet and have not have any replies and I'll be greatfull for any help.

Thanks.