Let
\[z = \frac{(-11 + 13i)^3 \cdot (24 - 7i)^4}{3 + 4i},\]and let $w = \frac{\overline{z}}{z}.$  Compute $|w|.$
I notice that $w$ is the ratio of the conjugate of $z$ to $z$ itself, which means that $w$ has the same modulus (or absolute value) as $\frac{z}{z} = 1.$ Therefore, $|w| = 1$ and I don't need to do any further calculations. 