The imaginary tetration unit? ssroot of -1 JmsNxn Ultimate Fellow Posts: 1,056 Threads: 121 Joined: Dec 2010 07/15/2011, 02:36 AM (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 Administrator Posts: 1,616 Threads: 102 Joined: Aug 2007 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 $\omega^\omega = -1$? $(-1)^{-1}=-1$? JmsNxn Ultimate Fellow Posts: 1,056 Threads: 121 Joined: Dec 2010 07/15/2011, 05:12 PM (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 $\omega^\omega = -1$? $(-1)^{-1}=-1$? 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 $^ff = -1$ « Next Oldest | Next Newest »

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