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+--- 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
\( ^ff = -1 \)