\rbqquest{For any complex number $a+bi$, you can compute that the
  solution to $$z'=(a+bi)z, \qquad z(0)=1$$ is:
\[e^{(a+bi)t}=e^{at}\left(\cos bt + i\sin bt\right).\]
The magnitude of $e^{(a+bi)t}$ is $e^{at}$, and the argument of $e^{(a+bi)t}$ is $bt$.
When $a>0$ and $b>0$, we can think of $e^{(a+bi)t}$ as a point in the
complex plane which traces out a path as $t$ varies.

The curve in the complex plane traced out by 
\[e^{(1+2\pi i)t}\]
most closely resembles which of the following?
}

\rbqchoice{
\begin{enumerate}[a)]
\item A straight ray along the positive real axis
\item A circle with radius $e$ and center at the origin
\item A circle with radius 1 and center at the origin
\item A spiral moving inwards and counterclockwise
\item A spiral moving outwards and counterclockwise
\item A spiral moving inwards and clockwise
\item A spiral moving outwards and counterclockwise
\end{enumerate}
}

\rbqans{
The magnitude of $e^{(1+2\pi i)t}$ is $e^t$ and the argument is $2\pi t$, so the answer is (e).
}
