[[Complex analysis MOC]]
# Complex numbers

The **complex numbers** $\mathbb{C}$ are the [[Algebraic closure]] of [[Real numbers]] #m/def/complex 
given by adjoining a single root of unity $i$ such that $i^2 = -1$, i.e.
$$
\begin{align*}
\mathbb{C} = \mathbb{R}[i]
\end{align*}
$$
Equivalently, $\mathbb{C}$ is the [[metric completion]] of the field of [[Number field|algebraic numbers]] $\overline{\mathbb{Q}}$.


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