Let $z$ be a complex number satisfying $z^2 = 4z - 19 + 8i$. Given that $|z|$ is an integer, find $z.$
Question:
Let $z$ be a complex number satisfying $z^2 = 4z - 19 + 8i$. Given that $|z|$ is an integer, find $z.$
Answer:
Let's think step by step.

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3 + 4i
Let $z$ be a complex number satisfying $z^2 = 4z - 19 + 8i$. Given that $|z|$ is an integer, find $z.$
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