\(\mathbb Z\) Complex Minima

Algebra Level 3

If \(Z\) is a non-zero complex number, then find the minimum value of

\[\displaystyle \dfrac{\text{Im}(Z^{5})}{(\text{Im}(Z))^{5} }.\]

Clarification: \(\text{Im}(Z)\) represent the imaginary part of \(Z\).

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