i, the power of the imaginary

Necessity makes the law, as they say, and in mathematics this is indeed often the case. Even when an idea seems absurd, if it proves useful then it ends up finding its place. The number i, this "number whose square equals −1" that the rule of signs forbids from existing, is among them. Certain results obtained with it were questionable or even inconsistent. Above all, one could not form a concrete representation of it. Its initiators such as Bombelli, in the Italian Renaissance, were certainly far from imagining that the computational oddity they used with caution would one day be elevated to the rank of fundamental constant of algebra.