# Field Extension/Examples/Complex Numbers over Reals

## Examples of Field Extensions

The complex numbers $\C$ forms a finite field extension over the real numbers $\R$ of degree $2$.

## Proof

It follows from Real Numbers form Subfield of Complex Numbers that $\C$ is an extension of $\R$.

From Vector Space over Division Subring: Real Numbers in Complex Numbers we have that the dimension of the vector space on $\C$ over $\R$ is $2$.

$\blacksquare$