9000034308
Parte:
C
Dos soluciones de la ecuación
\[
x^{3} + 1 + \mathrm{i} = 0
\]
son
\[
\begin{aligned}x_{1}& = \root{6}\of{2}\left (\cos \frac{5}
{12}\pi + \mathrm{i}\sin \frac{5}
{12}\pi \right ),&
\\x_{2}& = \root{6}\of{2}\left (\cos \frac{13}
{12}\pi + \mathrm{i}\sin \frac{13}
{12}\pi \right ).
\\ \end{aligned}
\]
Calcula la tercera solución.
\(x_{3} = \root{6}\of{2}\left (\cos \frac{21}
{12}\pi + \mathrm{i}\sin \frac{21}
{12}\pi \right )\)
\(x_{3} = \root{6}\of{2}\left (\cos \frac{9}
{12}\pi + \mathrm{i}\sin \frac{9}
{12}\pi \right )\)
\(x_{3} = \root{6}\of{2}\left (\cos \frac{17}
{12}\pi + \mathrm{i}\sin \frac{17}
{12}\pi \right )\)
\(x_{3} = \root{6}\of{2}\left (\cos \frac{19}
{12}\pi + \mathrm{i}\sin \frac{19}
{12}\pi \right )\)