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Construct the field of complex numbers as an extension of the field of rationales. Please, be...

Construct the field of complex numbers as an extension of the field of rationales. Please, be thorough.

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How to construct a field of complex numbers as an extension of the field of rationales?
How to construct a field of complex numbers as an extension of the field of rationales?
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Let E/F be a field extension. Let a,b be elements elements of E and algebraic over...
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