It’s not that it doesn’t exist, it’s just not a “real” number, doesn’t mean it’s fake or it’s made up, just it doesn’t belong among regular numbers, they have their own space we call the complex plane
Many things in physics are best described and calculated by using complex numbers, for example electronic circuits with capacitors and inductors are used all the time as oscillators and the equations that calculate that produce square roots of negative numbers, but with complex numbers, we can make sense of it and describe what actually happens
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