[SideQuark]

They’re more than useful: they’re required, hence the research demonstrating it that I linked. That you don’t understand it doesn’t mean the rest of science is at your level of ignorance on the topic.

Your repeated, willful ignorance on a topic, especially when shown to you, is why you have such low understanding of the incorrect claims you make.

Take a moment and learn. Then maybe you’ll not repeat claims shown to be wrong.

[nivertech]

I never agreed or disputed whether they're required or not, what I asked was whether they (complex numbers) were ever observed in Nature

[SideQuark]

Yes, they have been observed in the same rigor as any number you claim has been observed. If you’d spend a moment and read instead of repeated willful ignorance, you’d learn something.

Now go do your homework. Attaching idiot phrases like complex apples is as stupid as claiming we don’t see radio waves so they can’t exist or that matter cannot be mostly empty space because you can stack books.

Your limited imagination, understanding, and unwillingness to learn, even when given a source and phrases to look into, doesn’t apply to those scientists that have done the work.

[nivertech]

> Yes, they have been observed

Any references?