Problema 18

Demuestra que $ \forall a \in \mathbb{R}^{2}, \lvert a \rvert^{2} = a^{2} $

Demostración $$ \begin{align*} \lvert a \rvert^{2} & = (\sqrt{a^{2}})^{2} \\ & = ((a^{2})^{\frac{1}{2}})^{2} \\ & = a^{2} \end{align*} $$ $ \blacksquare $