Řešení binomické rovnice v goniometrickém tvaru
Urči kořeny binomické rovnice v goniometrickém tvaru:
\( -2 x^{8}-\sqrt{2}-i \sqrt{2}=0 \)
\( \begin{aligned} K= & \left\{\cos \frac{5 \pi}{32}+i \sin \frac{5 \pi}{32} ; \cos \frac{13 \pi}{32}+i \sin \frac{13 \pi}{32} ; \cos \frac{21 \pi}{32}+i \sin \frac{13 \pi}{32}\right. \\ & \cos \frac{29 \pi}{32}+i \sin \frac{29 \pi}{32} ; \cos \frac{37 \pi}{32}+i \sin \frac{37 \pi}{32} ; \cos \frac{45 \pi}{32}+i \sin \frac{45 \pi}{32} \\ & \left.\cos \frac{53 \pi}{32}+i \sin \frac{53 \pi}{32} ; \cos \frac{61 \pi}{32}+i \sin \frac{61 \pi}{32}\right\}\end{aligned} \)
\( \begin{aligned} K= & \left\{\cos \frac{7 \pi}{32}+i \sin \frac{7 \pi}{32} ; \cos \frac{15 \pi}{32}+i \sin \frac{15 \pi}{32} ; \cos \frac{23 \pi}{32}+i \sin \frac{23 \pi}{32}\right. \\ & \cos \frac{31 \pi}{32}+i \sin \frac{31 \pi}{32} ; \cos \frac{39 \pi}{32}+i \sin \frac{39 \pi}{32} ; \cos \frac{47 \pi}{32}+i \sin \frac{47 \pi}{32} \\ & \left.\cos \frac{55 \pi}{32}+i \sin \frac{55 \pi}{32} ; \cos \frac{63 \pi}{32}+i \sin \frac{63 \pi}{32}\right\}\end{aligned} \)
\( \begin{aligned} K= & \left\{\cos \frac{3 \pi}{32}+i \sin \frac{3 \pi}{32} ; \cos \frac{11 \pi}{32}+i \sin \frac{11 \pi}{32} ; \cos \frac{19 \pi}{32}+i \sin \frac{19 \pi}{32}\right. \\ & \cos \frac{27 \pi}{32}+i \sin \frac{27 \pi}{32} ; \cos \frac{35 \pi}{32}+i \sin \frac{35 \pi}{32} ; \cos \frac{43 \pi}{32}+i \sin \frac{43 \pi}{32} \\ & \left.\cos \frac{51 \pi}{32}+i \sin \frac{51 \pi}{32} ; \cos \frac{59 \pi}{32}+i \sin \frac{59 \pi}{32}\right\}\end{aligned} \)
\( \begin{aligned} K= & \left\{\cos \frac{9 \pi}{32}+i \sin \frac{9 \pi}{32} ; \cos \frac{17 \pi}{32}+i \sin \frac{17 \pi}{32} ; \cos \frac{25 \pi}{32}+i \sin \frac{25 \pi}{32}\right. \\ & \cos \frac{33 \pi}{32}+i \sin \frac{33 \pi}{32} ; \cos \frac{41 \pi}{32}+i \sin \frac{41 \pi}{32} ; \cos \frac{49 \pi}{32}+i \sin \frac{49 \pi}{32} \\ & \left.\cos \frac{57 \pi}{32}+i \sin \frac{57 \pi}{32} ; \cos \frac{65 \pi}{32}+i \sin \frac{65 \pi}{32}\right\}\end{aligned} \)