Určení kořenů binomické rovnice
Urči kořeny binomické rovnice a zapiš je v goniometrickém tvaru:
\large x^5-2+2\text{i} = 0
\large K = \left \{\sqrt [ 10] {8} \left( \cos {\Large \frac{11\pi}{20}\large }+\text{i}\sin {\Large \frac{11\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{19\pi}{20}\large }+\text{i}\sin {\Large \frac{19\pi}{20}\large }\right) ; \sqrt [ 10] {8} \left( \cos {\Large \frac{27\pi}{20}\large }+\text{i}\sin {\Large \frac{27\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{35\pi}{20}\large }+\text{i}\sin {\Large \frac{35\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{43\pi}{20}\large }+\text{i}\sin {\Large \frac{43\pi}{20}\large }\right) \right \}
\large K = \left \{\sqrt [ 10] {8} \left( \cos {\Large \frac{7\pi}{20}\large }+\text{i}\sin {\Large \frac{7\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{15\pi}{20}\large }+\text{i}\sin {\Large \frac{15\pi}{20}\large }\right) ; \sqrt [ 10] {8} \left( \cos {\Large \frac{23\pi}{20}\large }+\text{i}\sin {\Large \frac{23\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{31\pi}{20}\large }+\text{i}\sin {\Large \frac{31\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{39\pi}{20}\large }+\text{i}\sin {\Large \frac{39\pi}{20}\large }\right) \right \}
\large K = \left \{\sqrt [ 10] {8} \left( \cos {\Large \frac{5\pi}{20}\large }+\text{i}\sin {\Large \frac{5\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{13\pi}{20}\large }+\text{i}\sin {\Large \frac{13\pi}{20}\large }\right) ; \sqrt [ 10] {8} \left( \cos {\Large \frac{21\pi}{20}\large }+\text{i}\sin {\Large \frac{21\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{29\pi}{20}\large }+\text{i}\sin {\Large \frac{29\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{37\pi}{20}\large }+\text{i}\sin {\Large \frac{37\pi}{20}\large }\right) \right \}
\large K = \left \{\sqrt [ 10] {8} \left( \cos {\Large \frac{9\pi}{20}\large }+\text{i}\sin {\Large \frac{9\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{17\pi}{20}\large }+\text{i}\sin {\Large \frac{17\pi}{20}\large }\right) ; \sqrt [ 10] {8} \left( \cos {\Large \frac{25\pi}{20}\large }+\text{i}\sin {\Large \frac{25\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{33\pi}{20}\large }+\text{i}\sin {\Large \frac{33\pi}{20}\large }\right) ;\sqrt [ 10] {8} \left( \cos {\Large \frac{41\pi}{20}\large }+\text{i}\sin {\Large \frac{41\pi}{20}\large }\right) \right \}