How do I find the magnitude of the following: $G(jw) = \frac{jw}{(10^4 + jw)}$
I have tried to take multiply the numerator and denominator by $-jw$ to ultimately come up with $w/(\sqrt{w^2 + 10^8})$ as my final answer, but that doesn't seem like the right approach.
For a complex number $z$ we have
$$ |z| = \sqrt{z\cdot \bar z} $$
then
$$ |G(j\omega)| = \sqrt{\left(\frac{j\omega}{10^4+j\omega}\right)\left(\frac{-j\omega}{10^4-j\omega}\right)} = \frac{\omega}{\sqrt{10^8+\omega^2}} $$