Example 9.8.2. The field $\mathbf{C}$ is algebraic over $\mathbf{R}$. Namely, if $\alpha = a + ib$ in $\mathbf{C}$, then $\alpha ^2 - 2a\alpha + a^2 + b^2 = 0$ is a polynomial equation for $\alpha $ over $\mathbf{R}$.

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