Area of an \(n\)-gon on the Complex Plane

Algebra Level 4

When the roots of \(x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1\) and \(1\) are simultaneously graphed on the complex plane, a regular \(n\)-gon is formed with area \(q\). Find \(n+q\) rounded to the nearest integer.

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