Let $z = a + bi,$ where $a$ and $b$ are positive real numbers.  If
\[z^3 + |z|^2 + z = 0,\]then enter the ordered pair $(a,b).$
Question:
Let $z = a + bi,$ where $a$ and $b$ are positive real numbers.  If
\[z^3 + |z|^2 + z = 0,\]then enter the ordered pair $(a,b).$
Answer:
Let's think step by step.

user
\left( \frac{1}{2}, \frac{\sqrt{7}}{2} \right)
Let $z = a + bi,$ where $a$ and $b$ are positive real numbers.  If
\[z^3 + |z|^2 + z = 0,\]then enter the ordered pair $(a,b).$
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