\[\begin{equation} e^{ix} = \cos{x} + i\sin{x} \nonumber \end{equation}\]

\[\begin{equation} {(\cos{x} + i\sin{x})}^n = \cos{nx} + i\sin{nx} \nonumber \end{equation}\]

\[\begin{equation} \begin{pmatrix} \cos{\phi} & \sin{\phi} \\\ -\sin{\phi} & \cos{\phi} \end{pmatrix}^n = \begin{pmatrix} \cos{n\phi} & \sin{n\phi} \\\ -\sin{n\phi} & \cos{n\phi} \end{pmatrix} \nonumber \end{equation}\]