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g(z) = z^{87} + 36z^{57} + 71z^{4} + z^3 - z + 1

$$

For $|z|<1$.

Let $f(z) = 71z^4$.

Then $|f(z) - g(z)| = |-z^{87} - 36z^{57} - z^3 + z - 1| \leq |z|^{87} + 36|z|^{57} + |z|^3 + |z| + 1 < 71|z^4|$

So g has the same number of zeros as f which is 0 with multiplicity of 4.

Correct?