And an important note about imaginary numbers is there more of a band aid solution because we chose to lose information when doing positive exponentials, when in reality both positive and negative answers are equally valid mathematically (though sometimes not physically).

So math doesn’t care about our conventions and sometimes we need that information back, hence complex numbers.

Multiplying anything times 0 = 0 though doesn’t just have 2 possible outcomes, it has infinite for the variable multiplied. With such aggressive information loss its usually hard to retain any realistic information, though it is possible with proper limits