linguistic:translation, stylistic:style_transfer
2 × 2 matrices

With matrices, (cos ϕ − sin ϕ sin ϕ cos ϕ) n = (cos n ϕ − sin n ϕ sin n ϕ cos n ϕ) {\displaystyle {\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}}} when n is an integer. This is a direct consequence of the isomorphism between the matrices of type (a − b b a) {\displaystyle {\begin{pmatrix}a&-b\\b&a\end{pmatrix}}} and the complex plane.