>>11605304>what is the pointthe point is twofold. Our initial motivation is to understand the plane geometrically, but the real numbers do not admit necessarily nice properties in regards to rotation and scaling. The complex plane, however, has very nice results about how we can talk about these operations in natural setting.
On a more immediately practical level, the relationship between sets without i (such as the integers, rationals, etc) can be well understood when you adjoin i to them via a ring quotient. This formally constructs i in a way that is completely consistent with the rest of our mathematics, and it basically extends our understanding of these sets as a number line to understanding their properties as a lattice. We get some really succinct results on the original sets as a consequence.
tl;dr i is perfectly fine, but you likely don't understand how it's constructed formally
