1) express $\dfrac{30+19i}{4+9i}$ in the form $a + bi$, where $a$ and $b$ are real numbers.

2) for what real number $k$ does the product $(25 + ki)(3+2i)$ equal a real number?

3) what constant must we place in the box below in order to be able to factor the resulting expression into the product of two linear factors:
\[2mn - 16m - 7n + \boxed{\phantom{00}}? \]

4) how many pairs of integers $(b, c)$ satisfy the equation
\[\frac{b + 7}{b + 4} = \frac{c}{9}? \]

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