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MATH / Let P be the convex polygon in the complex plane whose vertices are the roots of z⁷+z⁶+z⁵+z⁴+z³+z²+z+1=0.The area of P can be expressed in the form (a+b√(c))/(d), where a, b, c, d …

Problem

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problem

Let PP be the convex polygon in the complex plane whose vertices are the roots of z7+z6+z5+z4+z3+z2+z+1=0.z^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 a,a, b,b, c,c, dd are positive integers, in simplest form. Find a+b+c+d.a + b + c + d.
Plain-text mathematical notation (without MathML)
Let P be the convex polygon in the complex plane whose vertices are the roots of
z⁷+z⁶+z⁵+z⁴+z³+z²+z+1=0.The area of P can be expressed in the form (a+b√(c))/(d), where a, b, c, d are positive integers, in simplest form.  Find a+b+c+d.
Original LaTeX notation
Let $P$ be the convex polygon in the complex plane whose vertices are the roots of
\[z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1 = 0.\]The area of $P$ can be expressed in the form $\frac{a + b \sqrt{c}}{d},$ where $a,$ $b,$ $c,$ $d$ are positive integers, in simplest form.  Find $a + b + c + d.$

level

Level 4

type

Precalculus

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Source and history

task_id
46d58ae4-a28f-57df-b117-8f635a68abed
task_key
precalculus--test--46d58ae4-a28f-57df-b117-8f635a68abed
task_revision_id
1
config / split
precalculus / test

Official source

initial import