benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Let z₁, z₂, z₃, and z₄ be the four distinct complex solutions of the equation z⁴−6z²+8z+1=−4(z³−z+2)i.Find the sum of the six pairwise distances between z₁, z₂, z₃, and z₄ in the c…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let z1,z_1, z2,z_2, z3,z_3, and z4z_4 be the four distinct complex solutions of the equation z4−6z2+8z+1=−4(z3−z+2)i. z^4 - 6z^2 + 8z + 1 = -4(z^3 - z + 2)i. Find the sum of the six pairwise distances between z1,z_1, z2,z_2, z3,z_3, and z4z_4 in the complex plane.
Plain-text mathematical notation (without MathML)
Let z₁, z₂, z₃, and z₄ be the four distinct complex solutions of the equation
z⁴−6z²+8z+1=−4(z³−z+2)i.Find the sum of the six pairwise distances between z₁, z₂, z₃, and z₄ in the complex plane.
Original LaTeX notation
Let $z_1,$ $z_2,$ $z_3,$ and $z_4$ be the four distinct complex solutions of the equation
\[
  z^4 - 6z^2 + 8z + 1 = -4(z^3 - z + 2)i.
\]Find the sum of the six pairwise distances between $z_1,$ $z_2,$ $z_3,$ and $z_4$ in the complex plane.

level

Level 5

type

Intermediate Algebra

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
b24abc9d-ceed-5eea-8173-c707c3f9d16d
task_key
intermediate~5falgebra--test--b24abc9d-ceed-5eea-8173-c707c3f9d16d
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import