Question 7
For integers $a$ and $b$ consider the complex number $$
\frac{\sqrt{ab + 2016}}{ab + 100} - \left(\frac{\sqrt{|a + b|}}{ab + 100}\right)i.
$$ Find the number of ordered pairs of integers $(a, b)$ such that this complex number is a real number.
\frac{\sqrt{ab + 2016}}{ab + 100} - \left(\frac{\sqrt{|a + b|}}{ab + 100}\right)i.
$$ Find the number of ordered pairs of integers $(a, b)$ such that this complex number is a real number.