# 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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