how do imaginary numbers work, and what are they used for
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Imaginary numbers are what happens when you try to take the square root of a negative number – there is no real number, positive or negative, rational or irrational or integer or prime or any other classification, that will give you a negative number when you square it, because a negative number times a negative number *always* yields a positive result, therefore a negative number times *itself* will always yield a positive result.
However, this was a problem when we ran into formulae that broke down when negative numbers were put in and used in a square root function, and there were practical situations where negative numbers in those cases were needed, so we worked around it with imaginary numbers.
An imaginary number is noted by the lower case “i”, and you treat this “i” as an algebraic variable (like the ubiquitous “x” that is used almost everywhere there isn’t another standard, or you need a second variable name) in almost every situation, except that i^2 = -1
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