Complex numbers are simply a mundane promise to multiply out your i at some future date, arguably. Much in the same way that a negative number is a promise to s

Complex numbers are simply a mundane promise to multiply out your i at some future date, arguably. Much in the same way that a negative number is a promise to square your books eventually at the end of the day. If you have a balance of -10 dollars the implication is that you'll give someone 10 dollars some day before they try to spend that money (for example). If you are trying to factor a polynomial with complex roots, is not a coincidence they appear in pairs which cancel out eventually, if you want to get back to a "real" value implied by the polynomial.