Formel von Moivre

Eine komplexe Zahl in Polarform wird mit einer natürlichen Zahl n folgendermaßen potenziert: ( r ⋅ e i ⋅ φ ) n = r n ⋅ e i ⋅ n φ MathType@MTEF@5@& 053;@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabe qaamaaeaqbaaGcbaWaaeWaaeaacaqGYbGaeyyXICTaaeyzamaaCaaa leqabaGaamyAaiabgwSixlabeA8aQbaaaOGaayjkaiaawMcaamaaCa aaleqabaGaamOBaaaakiaabccacaqG9aGaaeiiaiaabkhadaahaaWc beqaaiaad6gaaaGccqGHflY1caqGLbWaaWbaaSqabeaacaWGPbGaey yXICTaamOBaiabeA8aQbaaaaa@565F@ bzw. [ r ( cos φ + i ⋅ sin φ ) ] n = r n ( cos ( n φ ) + i ⋅ sin ( n φ ) ) MathType@MTEF@5@& 053;@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabe qaamaaeaqbaaGcbaWaamWaaeaacaWGYbWaaeWaaeaaciGGJbGaai4B aiaacohacqaHgpGAcqGHRaWkcaWGPbGaeyyXICTaci4CaiaacMgaca GGUbGaeqOXdOgacaGLOaGaayzkaaaacaGLBbGaayzxaaWaaWbaaSqa beaacaWGUbaaaOGaaeiiaiaab2dacaqGGaGaamOCamaaCaaaleqaba GaamOBaaaakmaabmaabaGaci4yaiaac+gacaGGZbWaaeWaaeaacaWG UbGaeqOXdOgacaGLOaGaayzkaaGaey4kaSIaamyAaiabgwSixlGaco hacaGGPbGaaiOBamaabmaabaGaamOBaiabeA8aQbGaayjkaiaawMca aaGaayjkaiaawMcaaaaa@67AF@</annotation> Die