Since I was interested in maths, I have a question. Is infinity a real or complex quantity? Or it isn't real or complex?
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There are many different things that could be called "the infinite" in mathematics. None of them is a real number or a complex number, but some are used in discussing functions or real or complex numbers.
The question is a bit meaningless. "The infinite" is a philosophical concept. There are a wide variety of very different mathematical objects that are used to represent "the infinite", and now that we're in the realm of mathematics and not philosophy, I can make the concrete mathematical claim that no, those objects are neither real numbers nor complex numbers.
For a rundown on what different mathematical objects can represent infinity, I think the linked questions in Asaf's comment under your question are a fine place to start.