# 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}.

x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 = 0