The equation Δis² = Δix² + Δiy² + Δiz² + Δit² does not represent a valid equation in the context of complex spacetime. In special relativity, spacetime is described by a four-dimensional manifold known as Minkowski spacetime, where the interval between two events is given by:
Δs² = Δt² - Δx² - Δy² - Δz²
This equation is known as the Minkowski metric or spacetime interval. It represents the spacetime interval between two events in terms of their temporal (Δt) and spatial (Δx, Δy, Δz) separations. The minus signs in front of the spatial terms are essential to ensure that the spacetime interval is invariant under Lorentz transformations.
The equation you provided, Δis² = Δix² + Δiy² + Δiz² + Δit², seems to introduce a different metric with a plus sign in front of the time term (Δit²). This would not be consistent with the standard formulation of spacetime in special relativity.
While there are alternative approaches and theories that introduce complex numbers in the context of spacetime, such as complexified Minkowski spacetime or complexified general relativity, the equation you provided does not appear to correspond to any established framework or representation of complex spacetime.