benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Let z=a+bi be the complex number with vert z vert = 5 and b>0 such that the distance between (1+2i)z³ and z⁵ is maximized. Compute z⁴.

Problem

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

problem

Let z=a+biz=a+bi be the complex number with $\vert z \vert = 5$ and b>0b > 0 such that the distance between (1+2i)z3(1+2i)z^3 and z5z^5 is maximized. Compute z4.z^4.
Plain-text mathematical notation (without MathML)
Let z=a+bi be the complex number with $\vert z \vert = 5$ and b>0 such that the distance between (1+2i)z³ and z⁵ is maximized. Compute z⁴.
Original LaTeX notation
Let $z=a+bi$ be the complex number with $\vert z \vert = 5$ and $b > 0$ such that the distance between $(1+2i)z^3$ and $z^5$ is maximized. Compute $z^4.$

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
a684df7d-bdb8-5ba8-ab28-e8db6495529f
task_key
intermediate~5falgebra--test--a684df7d-bdb8-5ba8-ab28-e8db6495529f
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import