@acer Thank you for the hint with the specfunc. I will use that for now, even though it still feels kindof "hacky". The RootFinding:-Isolate has required a lot of resources on some of my examples, that is why I avoided it. But maybe I will do a mix of both.

Thanks again.

@Alejandro Jakubi I agree... This would be something that I more expect.

@Axel Vogt As I wrote up there

"[...] I know that this system has no real solutions, but only complex ones.[...]"

The problem is rather how I handle this output in an automated routine as "no solution found by Maple's fsolve". But thanks for the theoretical excursion.