So many sides

If line segments are drawn from the origin of the complex plane to each of the solutions of $x^n = 1$ , and consecutive solutions are also connected by line segments we obtain $n$ isosceles triangles in a regular $n$ -gon. Let $a+bi$ be the solution with the smallest possible positive argument. If $\arctan{\left(\dfrac{b}{a}\right)} = \dfrac{\pi}{90}$ , then find the value of $n$ .