Here's a little bit of premise:
I'm working on a research project trying to design a distance function that generates both complex-valued and real "distances". I would like to see if for all real values my function produces if the euclidean triangle inequality holds. I was wondering if someone might help with what such an experiment would look like. Given three values with real distances from the origin, would I examine d(0,a), d(0,b), and d(0,c)?
Any insight appreciated
What do you mean "generates complex-valued and real 'distances' "? You cannot have a complex-valued distance, the complex numbers are not an ordered field. What do you mean by "generates"?