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MATH / The solutions of the equation z⁴+4z³i−6z²−4zi−i=0 are the vertices of a convex polygon in the complex plane. The area of this polygon can be expressed in the form p^(a/b), where a,…

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problem

The solutions of the equation z4+4z3i−6z2−4zi−i=0z^4+4z^3i-6z^2-4zi-i=0 are the vertices of a convex polygon in the complex plane. The area of this polygon can be expressed in the form pa/b,p^{a/b}, where a,a, b,b, pp are positive integers, pp is prime, and aa and bb are relatively prime. Find a+b+p.a + b + p.
Plain-text mathematical notation (without MathML)
The solutions of the equation z⁴+4z³i−6z²−4zi−i=0 are the vertices of a convex polygon in the complex plane.  The area of this polygon can be expressed in the form p^(a/b), where a, b, p are positive integers, p is prime, and a and b are relatively prime.  Find a+b+p.
Original LaTeX notation
The solutions of the equation $z^4+4z^3i-6z^2-4zi-i=0$ are the vertices of a convex polygon in the complex plane.  The area of this polygon can be expressed in the form $p^{a/b},$ where $a,$ $b,$ $p$ are positive integers, $p$ is prime, and $a$ and $b$ are relatively prime.  Find $a + b + p.$

level

Level 3

type

Precalculus

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Source and history

task_id
4ccd6c19-5ec3-58cf-b640-5bfdaf082443
task_key
precalculus--test--4ccd6c19-5ec3-58cf-b640-5bfdaf082443
task_revision_id
1
config / split
precalculus / test

Official source

initial import