Určení kořenů binomické rovnice
Urči kořeny binomické rovnice a zapiš je v goniometrickém tvaru:
\large x^6+1-\text{i}\sqrt {3} = 0
\large K = \left \{ \sqrt [ 6] {2} \left( \cos {\Large \frac{2\pi}{9}\large }+\text{i}\sin {\Large \frac{2\pi}{9}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{5\pi}{9}\large }+\text{i}\sin {\Large \frac{5\pi}{9}\large }\right) \sqrt [ 6] {2} \left( \cos {\Large \frac{8\pi}{9}\large }+\text{i}\sin {\Large \frac{8\pi}{9}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{11\pi}{9}\large }+\text{i}\sin {\Large \frac{11\pi}{9}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{14\pi}{9}\large }+\text{i}\sin {\Large \frac{14\pi}{9}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{17\pi}{9}\large }+\text{i}\sin {\Large \frac{17\pi}{9}\large }\right) \right \}
\large K = \left \{ \sqrt [ 6] {2} \left( \cos {\Large \frac{\pi}{9}\large }+\text{i}\sin {\Large \frac{\pi}{9}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{4\pi}{9}\large }+\text{i}\sin {\Large \frac{4\pi}{9}\large }\right) \sqrt [ 6] {2} \left( \cos {\Large \frac{7\pi}{9}\large }+\text{i}\sin {\Large \frac{7\pi}{9}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{10\pi}{9}\large }+\text{i}\sin {\Large \frac{10\pi}{9}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{13\pi}{9}\large }+\text{i}\sin {\Large \frac{13\pi}{9}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{16\pi}{9}\large }+\text{i}\sin {\Large \frac{16\pi}{9}\large }\right) \right \}
\large K = \left \{ \sqrt [ 6] {3} \left( \cos {\Large \frac{\pi}{9}\large }+\text{i}\sin {\Large \frac{\pi}{9}\large }\right) ;\sqrt [ 6] {3} \left( \cos {\Large \frac{4\pi}{9}\large }+\text{i}\sin {\Large \frac{4\pi}{9}\large }\right) \sqrt [ 6] {3} \left( \cos {\Large \frac{7\pi}{9}\large }+\text{i}\sin {\Large \frac{7\pi}{9}\large }\right) ;\sqrt [ 6] {3} \left( \cos {\Large \frac{10\pi}{9}\large }+\text{i}\sin {\Large \frac{10\pi}{9}\large }\right) ;\sqrt [ 6] {3} \left( \cos {\Large \frac{13\pi}{9}\large }+\text{i}\sin {\Large \frac{13\pi}{9}\large }\right) ;\sqrt [ 6] {3} \left( \cos {\Large \frac{16\pi}{9}\large }+\text{i}\sin {\Large \frac{16\pi}{9}\large }\right) \right \}
\large K = \left \{ \sqrt [ 6] {2} \left( \cos {\Large \frac{\pi}{8}\large }+\text{i}\sin {\Large \frac{\pi}{8}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{4\pi}{8}\large }+\text{i}\sin {\Large \frac{4\pi}{8}\large }\right) \sqrt [ 6] {2} \left( \cos {\Large \frac{7\pi}{8}\large }+\text{i}\sin {\Large \frac{7\pi}{8}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{10\pi}{8}\large }+\text{i}\sin {\Large \frac{10\pi}{8}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{13\pi}{8}\large }+\text{i}\sin {\Large \frac{13\pi}{8}\large }\right) ;\sqrt [ 6] {2} \left( \cos {\Large \frac{16\pi}{8}\large }+\text{i}\sin {\Large \frac{16\pi}{8}\large }\right) \right \}