# So many sides

Algebra Level 4

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 $$n$$.

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