To be sure, we also typically throw away imaginary roots when factoring polynomials, since they'd represent nonphysical solutions. But the imaginary bits do com

To be sure, we also typically throw away imaginary roots when factoring polynomials, since they'd represent nonphysical solutions. But the imaginary bits do come in handy for, well, nonphysical solutions, like measuring phase angle. So while I tend to side with you that the philosophy bit is probably unnecessary, I would contend that there may be surprising usefulness in the nonsense solutions (or they're just nonsense; it's hard to tell looking at the future work that hasn't been done yet).