Potęgi i pierwiastki liczb złożonych

\(- 1 -\mathrm{i}\sqrt{3}\)

\(1 + \mathrm{i}\sqrt{3}\)

\(- 2 -\mathrm{i}\sqrt{2}\)

\(2 + \mathrm{i}\sqrt{2}\)

\(8 - 8\mathrm{i}\)

\(7 - 7\mathrm{i}\)

\(1\)

\(-\mathrm{i}\)

\(\mathrm{i}\)

\(1 + 2\mathrm{i}\)

\(1 -\mathrm{i}\)

\(1\)

\(\begin{aligned}[t] &w_{0} = \root{6}\of{8}\left (\cos \frac{\pi } {4} + \mathrm{i}\sin \frac{\pi } {4}\right ) & \\&w_{1} = \root{6}\of{8}\left (\cos \frac{11\pi } {12} + \mathrm{i}\sin \frac{11\pi } {12}\right ) \\&w_{2} = \root{6}\of{8}\left (\cos \frac{19\pi } {12} + \mathrm{i}\sin \frac{19\pi } {12}\right ) \\ \end{aligned}\)

\(\begin{aligned}[t] &w_{0} = 2\left (\cos \frac{\pi } {4} + \mathrm{i}\sin \frac{\pi } {4}\right ) & \\&w_{1} = 2\left (\cos \frac{11\pi } {12} + \mathrm{i}\sin \frac{11\pi } {12}\right ) \\&w_{2} = 2\left (\cos \frac{19\pi } {12} + \mathrm{i}\sin \frac{19\pi } {12}\right ) \\ \end{aligned}\)

\(\root{3}\of{-2} + \root{3}\of{2}\)

\(\begin{aligned}[t] &w_{0} = 2\left (\cos \frac{\pi } {3} + \mathrm{i}\sin \frac{\pi } {3}\right )& \\&w_{1} = 2\left (\cos \pi +\mathrm{i}\sin \pi \right ) \\&w_{2} = 2\left (\cos \frac{5\pi } {3} + \mathrm{i}\sin \frac{5\pi } {3}\right ) \\ \end{aligned}\)