Evaluate $|2\omega^2-4\omega-30|$ if $\omega=1-5i$.
It's certainly possible to just calculate the complex number $2\omega^2-4\omega-30$ by just plugging in the value of $\omega$, but it's computationally simpler to use the fact that $|ab|=|a||b|$ and our knowledge of factoring quadratics: \begin{align*}
|2\omega^2-4\omega-30|&=|2(\omega-5)(\omega+3)|\\
&=2|\omega-5|\cdot|\omega+3|\\
&=2|-4-5i|\cdot|4-5i|\\
&=2\sqrt{(-4)^2+5^2}\sqrt{4^2+5^2}\\
&=\boxed{82}
\end{align*}