Let $a$ and $b$ be nonzero real numbers such that
\[(2 - 7i)(a + bi)\]is pure imaginary.  Find $\frac{a}{b}.$
Question:
Let $a$ and $b$ be nonzero real numbers such that
\[(2 - 7i)(a + bi)\]is pure imaginary.  Find $\frac{a}{b}.$
Answer:
Let's think step by step.

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-\frac{7}{2}
Let $a$ and $b$ be nonzero real numbers such that
\[(2 - 7i)(a + bi)\]is pure imaginary.  Find $\frac{a}{b}.$
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