X*X + 1 = 0 is a fundamental statement on an algebraic rings behavior with the additive and multiplicative identities and the additive and multiplicative group operations. Namely, it says that the ring contains an element that when multiplied by itself is equal to the additive inverse of the multiplicative identity . Plenty of rings have such an element. You can complete any ring with such an element and call it whatever you want. The use of the term imaginary for it is incredibly unfortunate. There's nothing strange or mystical about it. It's very real. In fact the rational complex numbers are more real than the non complex real numbers