Definition:Field Extension/Complex

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Definition

Let $\left({F, +, \times}\right)$ be a subfield of $\left({\Bbb C, +, \times}\right)$, the field of complex numbers.

Let $X_1, X_2, \ldots, X_n$ be complex numbers, in or not in $F$.

Then $F \left({X_1, X_2, \ldots, X_n}\right)$ is the smallest field extension over $F$ containing $X_1, X_2, \ldots, X_n$.