# Exercice 2
$$
\begin{align}
\ket{\psi} &= \frac{1}{\sqrt{ 2 }}[\ket{0} + e^{i\delta}\ket{1}] \\
&= \frac{1}{\sqrt{ 2 }}[\begin{pmatrix}
1 \\
0
\end{pmatrix} + e^{i \delta} \begin{pmatrix}
0 \\
1
\end{pmatrix}] \\
&= \frac{1}{\sqrt{ 2 }}\begin{pmatrix}
1 \\
e^{i\delta}
\end{pmatrix} \\
\bra{\psi} &= \frac{1}{\sqrt{ 2 }}[\bra{0} + e^{-i\delta}\bra{1}] \\
&= \frac{1}{\sqrt{ 2 }}[\begin{pmatrix}
1 \\
0
\end{pmatrix} + e^{-i \delta} \begin{pmatrix}
0 \\
1
\end{pmatrix}] \\
&= \frac{1}{\sqrt{ 2 }}\begin{pmatrix}
1 & e^{-i\delta}
\end{pmatrix}
\end{align}
$$
# Exercice 3