How many ordered pairs of solutions (a, b) are there to \frac{a}{b} - \frac{b}{a} - \frac{2}{a} - \frac{2}{b} = 0, where a and b are integers from -100 \leq a,b \leq 100?

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  1. Let $a,$ $b,$ $c$ be complex numbers such that\begin{align*} \frac{a}{b + c} + \frac{b}{c + a} + \frac{c}{a + b} &= 0, \\
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