A number that, when squared, is equal to minus one

At the beginning of the eight entry of We, D-503 describes learning about i when he was young. He recalls being distressed due to it "being outside of the ratio". This made me wonder about the history of i. As we know it, the irrationals are a subset of the reals, which themselves are a subset of the complex numbers... which is where i first shows up. I tried to imagine i as being "outside the ratio", but found it very difficult.
Also, I find it amusing that even in Zamyatin's wildest futuristic dreams, people still use ink pens (I'm writing this on my phone)