Let $z$ be a complex number with $|z| = \sqrt{2}.$  Find the maximum value of
\[|(z - 1)^2 (z + 1)|.\]
Question:
Let $z$ be a complex number with $|z| = \sqrt{2}.$  Find the maximum value of
\[|(z - 1)^2 (z + 1)|.\]
Answer:
Let's think step by step.

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4 \sqrt{2}
Let $z$ be a complex number with $|z| = \sqrt{2}.$  Find the maximum value of
\[|(z - 1)^2 (z + 1)|.\]
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