Introducing imaginary numbers doesn’t make it untrue that negative numbers don’t have a square root in the reals. Your analogy is more akin to maybe physicists

Introducing imaginary numbers doesn’t make it untrue that negative numbers don’t have a square root in the reals. Your analogy is more akin to maybe physicists will find something that can do nondeterministic computation in polynomial time—interesting in its own right but irrelevant to the mathematical problem as stated.