Everything makes sense when you see I for what it is -- an escape from the number line rotated by ninety degrees.
Even the roots of a parabola that doesn't hit the z axis are actually the roots of the ninety degree rotated inverse analogue hitting the imaginary plane. Since the apex of such a parabola is always centered at 0i, the imaginary places it hits are symmetric, explaining why if a + bi is one imaginary root, then a - bi is as well.
Again... There is nothing weird about imaginary numbers. They actually make a lot of sense. It's actually insane to only do math in one dimension when our world has three.
