The platform also supports {\tt problem} and {\tt solution} environments:

\begin{verbatim}
\begin{problem}
Given the complex number $z = e^{i\frac{2\pi}{3}}$, determine $\sqrt[4]{z}$ . Be mindful of how many fourth roots $z$ has and identify each 
of them.
\end{problem}

\begin{solution}
\begin{align*}
z &= e^{i\frac{2\pi}{3}} \\
z &= e^{i(\frac{2\pi}{3} + 2\pi k) } \mbox{ for some } k \in \Z \\
\sqrt[4]{z} &= e^{i(\frac{2\pi}{3} + 2\pi k) \frac{1}{4}} \\
\sqrt[4]{z} &= e^{i(\frac{\pi}{6} + \frac{\pi}{2} k) \frac{1}{4}} 
\end{align*}
So we can determine that within the range [$0,2\pi$), we find that $\sqrt[4]{z} = e^{i\frac{\pi}{6}}, e^{i\frac{2\pi}{3}}, e^{i\frac{7\pi}{6}}, e^{i\frac{5\pi}{3}}$
\end{solution}
\end{verbatim}

\begin{problem}
Given the complex number $z = e^{i\frac{2\pi}{3}}$, determine $\sqrt[4]{z}$ . Be mindful of how many fourth roots $z$ has and identify each 
of them.
\end{problem}

\begin{solution}
\begin{align*}
z &= e^{i\frac{2\pi}{3}} \\
z &= e^{i(\frac{2\pi}{3} + 2\pi k) } \mbox{ for some } k \in \Z \\
\sqrt[4]{z} &= e^{i(\frac{2\pi}{3} + 2\pi k) \frac{1}{4}} \\
\sqrt[4]{z} &= e^{i(\frac{\pi}{6} + \frac{\pi}{2} k) \frac{1}{4}} 
\end{align*}
So we can determine that within the range [$0,2\pi$), we find that $\sqrt[4]{z} = e^{i\frac{\pi}{6}}, e^{i\frac{2\pi}{3}}, e^{i\frac{7\pi}{6}}, e^{i\frac{5\pi}{3}}$
\end{solution}


problems and solutions