$\displaystyle \left[\vphantom{ {q \left( {\cos \varphi + i \sin \varphi } \right) } }\right.$q$\displaystyle \left(\vphantom{ {\cos \varphi + i \sin \varphi } }\right.$cos$\displaystyle \varphi$+i sin$\displaystyle \varphi$$\displaystyle \left.\vphantom{ {\cos \varphi + i \sin \varphi } }\right)$$\displaystyle \left.\vphantom{ {q \left( {\cos \varphi + i \sin \varphi } \right) } }\right]^{{{n }}}_{{}}$ = $\displaystyle \varphi^{{{n }}}_{{}}$$\displaystyle \left(\vphantom{ {\cos n \varphi +i \sin n \varphi } }\right.$cos n$\displaystyle \varphi$+i sin n$\displaystyle \varphi$$\displaystyle \left.\vphantom{ {\cos n \varphi +i \sin n \varphi } }\right)$ (1)