# 17th Root of Unity

Apr 12 2016

## Calculating the 17th Root of Unity

On the 17th root of unity, the following equation is known.

`cos((2pi)/17) = 1/16(-1 + sqrt 17 + sqrt (34 - 2 sqrt 17) + 2 sqrt (17 + 3 sqrt 17 - sqrt (34 - 2 sqrt 17) - 2 sqrt (34 + 2 sqrt 17)))`.
We calucuate this value in the following code.

We utilize the fact that the Galois group of the following equation has same structure with the multiplicative group of `ZZ//17ZZ-{0}`.