Why does (-1)*(-1)=(+1) ? It is arbitrary, and there really is no good reason. We could construct number lines that work differently, so that imaginary numbers never appear. Such alternative number lines would still allow us to solve the exact same physics and engineering problems. Sure, the computations would work differently, but the way we would measure and use the initial conditions in our equations would be different too. In the end, the predicted outcome would still be the same.
Imaginary numbers are an artifact of how our number line is constructed. We could construct alternative number lines where imaginary numbers do no exists. The computations involving such alternative number lines would be different, but the outcome would be the same.
Imaginary numbers are an artifact of how our number line is constructed. We could construct alternative number lines where imaginary numbers do no exists. The computations involving such alternative number lines would be different, but the outcome would be the same.