>>12674904One example of its mosts practical applications is in the field of electronics. There is a thing called reactance that is the imaginary part of a certain impedance. Its a concept very used in electronics and physics.
Im too lazy to explain it properly, so let me just indicate some concepts like, poles in signal filters, resonators, impedances matching in trasnmission guides, Fourier Series and Transform, PDE solutions...
In resume there is a shittons of things you can do with the imaginary numbers. You can see it as a tool like a hammer or a screwdriver, the value of it is in the things you can do with it not in itself.
Lastly Im gonna quote Gauss from Wikipedia because I really like him.
~If one formerly contemplated this subject from a false point of view and therefore found a mysterious darkness, this is in large part attributable to clumsy terminology. Had one not called +1, ?1, ??1 positive, negative, or imaginary (or even impossible) units, but instead, say, direct, inverse, or lateral units, then there could scarcely have been talk of such darkness.~ Gauss (1831)