The complex plane is given an orthonormal direct coordinate system $(\mathrm{O}; \vec{u}, \vec{v})$.\\
We consider the point A with affixe 4, the point B with affixe $4\mathrm{i}$ and the points C and D such that ABCD is a square with centre O.\\
For any non-zero natural number $n$, we call $M_n$ the point with affixe $z_n = (1 + \mathrm{i})^n$.

\begin{enumerate}
  \item Write the number $1 + \mathrm{i}$ in exponential form.
  \item Show that there exists a natural number $n_0$, which we will determine, such that, for any integer $n \geqslant n_0$, the point $M_n$ is outside the square ABCD.
\end{enumerate}