Algebraic Closure of Real Number Field is Complex Number Field

Theorem

Let $\R$ denote the field of real numbers.

Let $\C$ denote the field of complex numbers.

The algebraic closure of $\R$ is $\C$.

Proof

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Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): algebraically closed (algebraic closure)