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.
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.
