2. Let F be an ordered field. From the axioms of ordered fields presented in lecture,...

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2. Let F be an ordered field. From the axioms of ordered fields presented in lecture, prove that Va € F, a² + 1 > 0. Use this to argue that if a field F contains a solution to the equation x² + 1 = 0, then F cannot be ordered (in particular, there is no ordering on C that makes it into an ordered field). 2. Let F be an ordered field. From the axioms of ordered fields presented in lecture, prove that Va € F, a² + 1 > 0. Use this to argue that if a field F contains a solution to the equation x² + 1 = 0, then F cannot be ordered (in particular, there is no ordering on C that makes it into an ordered field).