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No ordinary, "real" number can give a negative result when squared.

Hence the equation EQN:x^2+4=0 has no solution.

This doesn't seem like such a problem, but the development of the

general solution to the cubic equation uses quantities of this

type, which then subsequently all cancel out leaving just real

solutions. Somehow these "imaginary" quantities seem to be useful.

Can they be added, subtracted, multiplied and divided like normal

numbers? Certainly they can be added and subtracted, but multiplying

two imaginary numbers gives a real number, so things only really work

when imaginary numbers are combined with the "normal" numbers. This

combination gives what are called the complex numbers.

The imaginary number EQN:i has the property EQN:i^2=-1