# Tetration Forum

Full Version: The imaginary tetration unit? ssroot of -1
You're currently viewing a stripped down version of our content. View the full version with proper formatting.
I was just wondering if anywhere anyone ever looked up a number such that $\omega^\omega = -1$, or $\omega = \text{SuperSquareRoot}(-1)$?

Is there a representation of $\omega$ using complex numbers?

I tried to work it out with the lambert W function but I'm not too good with it.

$\ln(\omega)\cdot \omega = \pi \cdot i$

I guess technically, there could be a different omega that is defined by:
$\ln(\omega)\cdot \omega = -\pi \cdot i$ and so on and so forth for all the possible values given by the multivalued nature of the logarithm.

I'm wondering what the principal value is, the one I first asked for.
(07/15/2011, 02:36 AM)JmsNxn Wrote: [ -> ]I was just wondering if anywhere anyone ever looked up a number such that $\omega^\omega = -1$?

$(-1)^{-1}=-1$?
(07/15/2011, 07:29 AM)bo198214 Wrote: [ -> ]
(07/15/2011, 02:36 AM)JmsNxn Wrote: [ -> ]I was just wondering if anywhere anyone ever looked up a number such that $\omega^\omega = -1$?

$(-1)^{-1}=-1$?

Ohhhhh my god! How did I miss that!?

I guess this kind of makes the square root of negative one more unique in my eyes.

however, there's still

$^ff = -1$