Find the sum of all complex numbers $z$ that satisfy
\[z^3 + z^2 - |z|^2 + 2z = 0.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the sum of all complex numbers $z$ that satisfy
\[z^3 + z^2 - |z|^2 + 2z = 0.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-2
Find the sum of all complex numbers $z$ that satisfy
\[z^3 + z^2 - |z|^2 + 2z = 0.\]
train