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+# 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