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evaluate cot(pi)

I know that on the unit circle, cot(pi) ends up as -1/0. In my precalc class, we say that this is undefined because you can't divide by zero.

I decided to plug the problem into wolfram and it tells me that there is in fact an answer, that being complex infinity.

I'm not sure what to make of this as I've never heard of complex infinity.

Am I wrong to say that cot(pi), or any other number divided by zero is undefined, or is the correct answer complex infinite?

Thanks!