A tourist takes a tour through a city in stages. Each stage consists of 3 segments of length 100 feet, separated by right turns of 60°. Between the last segment of one stage and the first segment of the next stage, the tourist makes a left turn of 60°. At what distance will the tourist be from his initial position after 2010 stages?
ε = e(π/3)i = cos(π/3) + i*sin(π/3) corresponds to a 60° turn to the left
ε6 = 1
The Attempt at a Solution
I really didn't know how to start, so my attempt might not even be relevant. I am also not very familiar with polar coordinates.
I started trying to do this algebraically, by assuming that e-(π/3)i corresponds to a 60° turn to the right. e-(π/3)i*e-(π/3)i*e(π/3)i since the tourist makes 2 right turns then a left in one stage. This equals e-(π/3)i. At this point, I don't know what to do next, or if I should even continue in this direction.