Let $z$ be a complex number satisfying $z^2 + z + 1 = 0.$  Compute
\[z^{97} + z^{98} + z^{99} + z^{100} + z^{101}.\]
Question:
Let $z$ be a complex number satisfying $z^2 + z + 1 = 0.$  Compute
\[z^{97} + z^{98} + z^{99} + z^{100} + z^{101}.\]
Answer:
Let's think step by step.

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-1
Let $z$ be a complex number satisfying $z^2 + z + 1 = 0.$  Compute
\[z^{97} + z^{98} + z^{99} + z^{100} + z^{101}.\]
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