Excellent. Indeed, as you say already for the real numbers one could have chosen sqrt(9) = -3: after all, (-3)^2 = 9 just as much as 3^2 = 9. Taking into accoun

Excellent. Indeed, as you say already for the real numbers one could have chosen sqrt(9) = -3: after all, (-3)^2 = 9 just as much as 3^2 = 9. Taking into account this inherent ambiguity in the definition of the square root function becomes crucial when extending it to the negative numbers, as my example shows. So, long story short: although not everyone agrees, personally I prefer to define the imaginary numbers by means of an entity i that obeys i^2 = -1, and avoid talking about "square roots of negative numbers" as the (otherwise fine) article does.