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## Homework Statement

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?

## Homework Equations

ε = e

^{(π/3)i}= cos(π/3) + i*sin(π/3) corresponds to a 60° turn to the left

ε

^{6}= 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.