I asked this question on MSE and comments suggested I should ask it here
I am currently reading Baby Rudin as my second analysis book (after Introduction to Real Analysis by Robert G. Bartle and Donald R. Sherbert) and I was surprised that Rudin’s book includes complex numbers, I tried to avoid complex numbers for a while because the way we were taught about them in school and even college was unsatisfactor They said something like "Mathematicians in the past didn’t accept complex numbers and thought they were meaningless and nonsense, but now they don't" and then moved on with the course without explaining why mathematicians in the past rejected complex numbers and what made them accept them later. This question has been on my mind for quite some time and I tried to avoid complex numbers as much as possible as this question is probably very hard to answer (after all, there must be a reason why we were not taught the answer to this question). But now, since I "have" to deal with complex numbers, I want to know the answer to this question. After some thought, I remembered that not only complex numbers was viewed as meaningless and nonsense then became normal, but also zero and negative numbers were not accepted and viewed as nonsense in the past, and then became normal.
So I want to ask for some references (books, articles, etc.) that explain what was the problem of accepting zero, negative numbers, and complex numbers, and how these problems were solved.
Jesse Madnick told me in the comments of my original question that
These problems were "solved" by humans understanding that mathematical ideas are just that: abstract concepts. All that's required for a mathematical object to exist is a precise definition and a rigorous proof of existence.
I want to ask what made modern mathematician think this way and when and how did this happen?