Z\mathbb Z Complex Minima

Algebra Level 3

If ZZ is a non-zero complex number, then find the minimum value of

Im(Z5)(Im(Z))5.\displaystyle \dfrac{\text{Im}(Z^{5})}{(\text{Im}(Z))^{5} }.

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

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