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JmsNxn · (This post was last modified: 07/15/2011, 02:38 AM by JmsNxn.)

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.

***bo198214*** · 07/15/2011, 07:29 AM

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

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

JmsNxn · (This post was last modified: 07/15/2011, 05:31 PM by JmsNxn.)

(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 $\omega^\omega = -1$ ?

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

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

$^ff = -1$

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