Complex analysis is an entire field of mathematics that focuses on the use of the complex constant $i$. When was the significance of $i$, an imaginary number, first noticed?
If I did not know some of the uses of complex analysis, I would likely believe, being the layman that I am, that $i$, as it is not a real number, would be fairly useless, almost like $0/0$. I would have trouble believing it had many uses, because it cannot be used to describe amounts of things like real numbers can (e.g. "I have 5 apples").
Why was any special attention paid to $i$ in the first place?
See this for a history of complex numbers and here for some motivation. Also there's a website on answers and explanations that explain concepts such as imaginary numbers and infinity.