Let $z$ be a complex number such that
\[z^5 + z^4 + 2z^3 + z^2 + z = 0.\]Find all possible values of $|z|.$

Enter all possible values, separated by commas.
Question:
Let $z$ be a complex number such that
\[z^5 + z^4 + 2z^3 + z^2 + z = 0.\]Find all possible values of $|z|.$

Enter all possible values, separated by commas.
Answer:
Let's think step by step.

user
0,1
Let $z$ be a complex number such that
\[z^5 + z^4 + 2z^3 + z^2 + z = 0.\]Find all possible values of $|z|.$

Enter all possible values, separated by commas.
train