The imaginary unit in algebra with respect to quadratic field extensions?
The question is whether i = sqrt(-1)? We consider the polynomial x^2 + 1 in R[x], or the quadratic equation x^2 + 1 = 0. This has a discriminant of -1 according to the quadratic solution formula. Since the discriminant in R is not a square, the equation in R is unsolvable. We adjoint the…