The imaginary tetration unit? ssroot of -1 - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: The imaginary tetration unit? ssroot of -1 (/showthread.php?tid=679) The imaginary tetration unit? ssroot of -1 - JmsNxn - 07/15/2011 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. RE: The imaginary tetration unit? ssroot of -1 - bo198214 - 07/15/2011 (07/15/2011, 02:36 AM)JmsNxn Wrote: I was just wondering if anywhere anyone ever looked up a number such that $\omega^\omega = -1$? $(-1)^{-1}=-1$? RE: The imaginary tetration unit? ssroot of -1 - JmsNxn - 07/15/2011 (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 $^ff = -1$