How do I simplify $|z^4 + iz + 1|$

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In general, I would like to know which is the best approach in solving this deg $4$ complex polynomial.

This seems too complex and I am missing something fundamental?

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$$|z^3+(-iz)+1|\le|z^3|+|-iz|+|1|=|z|^3+|-i||z|+1=3^3+1\cdot3+1$$

See : Useful Inequalities Among Complex Numbers