# 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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