Complex Function

Algebra Level 5

Let \(f: \mathbb{C}\mapsto \mathbb{C}\) be defined as \(f(z)=z^2+iz+1\) for all complex \(z\). How many complex numbers \(z\) are there such that \(\text{Im} (z) > 0\), and both the real and imaginary parts of \(f(z)\) are integers with absolute value of at most 10?

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