Level:
Project ID:
9000034308
Source Problem:
Accepted:
1
Clonable:
1
Easy:
0
Two solutions of the equation
\[
x^{3} + 1 + \mathrm{i} = 0
\]
are
\[
\begin{aligned}x_{1}& = \root{6}\of{2}\left (\cos \frac{5}
{12}\pi + \mathrm{i}\sin \frac{5}
{12}\pi \right ),&
\\x_{2}& = \root{6}\of{2}\left (\cos \frac{13}
{12}\pi + \mathrm{i}\sin \frac{13}
{12}\pi \right ).
\\ \end{aligned}
\]
Find the third solution.
\(x_{3} = \root{6}\of{2}\left (\cos \frac{21}
{12}\pi + \mathrm{i}\sin \frac{21}
{12}\pi \right )\)
\(x_{3} = \root{6}\of{2}\left (\cos \frac{9}
{12}\pi + \mathrm{i}\sin \frac{9}
{12}\pi \right )\)
\(x_{3} = \root{6}\of{2}\left (\cos \frac{17}
{12}\pi + \mathrm{i}\sin \frac{17}
{12}\pi \right )\)
\(x_{3} = \root{6}\of{2}\left (\cos \frac{19}
{12}\pi + \mathrm{i}\sin \frac{19}
{12}\pi \right )\)