A Complex Primitive $N$th Root Of Unity: A Very Elementary Approach
  This paper presents a primitive $n$th root of unity in $\mathbb C$. The approach is very elementary and avoids the following: the complex exponential function, trigonometry, and group theory. It also avoids differentiation, integration, and series. The presentation of the primitive is indirect. 
Oswaldo Rio Branco de Oliveira
math.CV