Řešení binomické rovnice v goniometrickém tvaru
Urči kořeny binomické rovnice v goniometrickém tvaru:
\( -2 x^{6}=-1+i \sqrt{3} \)
\( \begin{aligned} K= & \left\{\cos \frac{4 \pi}{18}+i \sin \frac{4 \pi}{18} ; \cos \frac{10 \pi}{18}+i \sin \frac{10 \pi}{18} ; \cos \frac{16 \pi}{18}+i \sin \frac{16 \pi}{18}\right. \\ & \left.\cos \frac{22 \pi}{18}+i \sin \frac{22 \pi}{18} ; \cos \frac{28 \pi}{18}+i \sin \frac{28 \pi}{18} ; \cos \frac{34 \pi}{18}+i \sin \frac{34 \pi}{18}\right\}\end{aligned} \)
\( \begin{aligned} K= & \left\{\cos \frac{6 \pi}{18}+i \sin \frac{6 \pi}{18} ; \cos \frac{12 \pi}{18}+i \sin \frac{12 \pi}{18} ; \cos \frac{18 \pi}{18}+i \sin \frac{18 \pi}{18}\right. \\ & \left.\cos \frac{24 \pi}{18}+i \sin \frac{24 \pi}{18} ; \cos \frac{30 \pi}{18}+i \sin \frac{30 \pi}{18} ; \cos \frac{36 \pi}{18}+i \sin \frac{36 \pi}{18}\right\}\end{aligned} \)
\( \begin{aligned} K= & \left\{\cos \frac{7 \pi}{18}+i \sin \frac{7 \pi}{18} ; \cos \frac{13 \pi}{18}+i \sin \frac{13 \pi}{18} ; \cos \frac{19 \pi}{18}+i \sin \frac{19 \pi}{18}\right. \\ & \left.\cos \frac{25 \pi}{18}+i \sin \frac{25 \pi}{18} ; \cos \frac{31 \pi}{18}+i \sin \frac{31 \pi}{18} ; \cos \frac{37 \pi}{18}+i \sin \frac{37 \pi}{18}\right\}\end{aligned} \)
\( \begin{aligned} K= & \left\{\cos \frac{5 \pi}{18}+i \sin \frac{5 \pi}{18} ; \cos \frac{11 \pi}{18}+i \sin \frac{11 \pi}{18} ; \cos \frac{17 \pi}{18}+i \sin \frac{17 \pi}{18}\right. \\ & \left.\cos \frac{23 \pi}{18}+i \sin \frac{23 \pi}{18} ; \cos \frac{29 \pi}{18}+i \sin \frac{29 \pi}{18} ; \cos \frac{35 \pi}{18}+i \sin \frac{35 \pi}{18}\right\}\end{aligned} \)