Určení kořenů binomické rovnice
Urči kořeny binomické rovnice:
\large \left( 1+\text{i}\right) x^2 = \text{i}
\large K = \left \{\Large \frac{\sqrt [ 4] {2^3}}{2}\large \left( \cos {\Large \frac{7\pi}{8}\large }+\text{i}\sin {\Large \frac{7\pi}{8}\large }\right) ;\Large \frac{\sqrt [ 4] {2^3}}{2}\large \left( \cos {\Large \frac{13\pi}{8}\large }+\text{i}\sin {\Large \frac{13\pi}{8}\large }\right) \right \}
\large K = \left \{\Large \frac{\sqrt [ 4] {2^3}}{2}\large \left( \cos {\Large \frac{3\pi}{8}\large }+\text{i}\sin {\Large \frac{3\pi}{8}\large }\right) ;\Large \frac{\sqrt [ 4] {2^3}}{2}\large \left( \cos {\Large \frac{11\pi}{8}\large }+\text{i}\sin {\Large \frac{11\pi}{8}\large }\right) \right \}
\large K = \left \{\Large \frac{\sqrt [ 4] {2^3}}{2}\large \left( \cos {\Large \frac{\pi}{8}\large }+\text{i}\sin {\Large \frac{\pi}{8}\large }\right) ;\Large \frac{\sqrt [ 4] {2^3}}{2}\large \left( \cos {\Large \frac{9\pi}{8}\large }+\text{i}\sin {\Large \frac{9\pi}{8}\large }\right) \right \}
\large K = \left \{\Large \frac{\sqrt [ 4] {2^3}}{2}\large \left( \cos {\Large \frac{\pi}{4}\large }+\text{i}\sin {\Large \frac{\pi}{4}\large }\right) ;\Large \frac{\sqrt [ 4] {2^3}}{2}\large \left( \cos {\Large \frac{5\pi}{8}\large }+\text{i}\sin {\Large \frac{5\pi}{8}\large }\right) \right \}