Polar Coordinates and Complex Numbers · Superchallenge problem

A robot starts at the origin facing the positive $x$-axis. It walks $1$ unit, turns $30^\circ$ to the left, walks $2$ units, turns $30^\circ$ to the left, walks $3$ units, and so on: on the $k$th walk it covers $k$ units, and it turns $30^\circ$ left after each walk. After its $12$th walk (of $12$ units) it stops. How far is it from the origin?