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A random question for mathematicians regarding i and the Fibonacci sequence. - Printable Version

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A random question for mathematicians regarding i and the Fibonacci sequence. - robo37 - 08/07/2011

What is the Fibonacci root of i, or to put it another way, what is the equation of x when ((1+sqrt 5)/2)^x-((-1)^x/((1+sqrt 5)/2)^x)))/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.