# AM-GM + Complex!

Algebra Level 4

If $$|z-4+3i| \leq 1$$ and $$\alpha, \beta$$ be the least and the greatest value of $$|z|$$ respectively and $$k$$ be the least value of $$\large \frac{x^4 + x^2 +4}{x}$$ on the interval $$(0,\infty)$$, then what is the value of $$k$$?

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