Mathegoras

Complex numbers › The complex plane › Extremes of the modulus

Area of polygon from cyclotomic roots

High school · ●●●○○ 50 pts

Let PP be the convex polygon in the complex plane whose vertices are the roots of z7+z6+z5+z4+z3+z2+z+1=0z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1 = 0. The area of PP can be expressed in the form a+bcd\frac{a + b \sqrt{c}}{d}, where aa, bb, cc, dd are positive integers, in simplest form. Find a+b+c+da + b + c + d.

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roots of unitypolygon areacyclotomic polynomials