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MATH / Let z be a nonreal complex number. Find the smallest possible value of

Problem

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problem

Let zz be a nonreal complex number. Find the smallest possible value of Im(z5)[Im(z)]5.\frac{\text{Im}(z^5)}{[\text{Im}(z)]^5}.Note: For a complex number z,z, Im(z)\text{Im}(z) denotes the imaginary part of z.z.
Plain-text mathematical notation (without MathML)
Let z be a nonreal complex number.  Find the smallest possible value of
(Im(z⁵))/([Im(z)]⁵).Note: For a complex number z, Im(z) denotes the imaginary part of z.
Original LaTeX notation
Let $z$ be a nonreal complex number.  Find the smallest possible value of
\[\frac{\text{Im}(z^5)}{[\text{Im}(z)]^5}.\]Note: For a complex number $z,$ $\text{Im}(z)$ denotes the imaginary part of $z.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
760a985d-874b-5895-80c1-cccfe0aa5873
task_key
intermediate~5falgebra--test--760a985d-874b-5895-80c1-cccfe0aa5873
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import