If $z$ is a complex number such that
\[
  z + z^{-1} = \sqrt{3},
\]what is the value of
\[
  z^{2010} + z^{-2010} \, ? 
\]
Question:
If $z$ is a complex number such that
\[
  z + z^{-1} = \sqrt{3},
\]what is the value of
\[
  z^{2010} + z^{-2010} \, ? 
\]
Answer:
Let's think step by step.

user
-2
If $z$ is a complex number such that
\[
  z + z^{-1} = \sqrt{3},
\]what is the value of
\[
  z^{2010} + z^{-2010} \, ? 
\]
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