Is this a valid method of finding magnitude of complex fraction If I have a complex fraction $\dfrac{a+bi}{c+di}$ and I want the magnitude, then will it be $\left|\dfrac{a+bi}{c+di}\right|=\dfrac{|a+bi|}{|c+di|}$?
Scratch that ... I just found the answer on another page; however, I'm still unclear why it's true?

A simpler approach:
Let $z_1=a+bi$ and $z_2=c+di$.  Since by properties of absolute value we have $|z_1z_2|=|z_1||z_2|,$ and the fact that $z_2(\frac{z_1}{z_2})=z_1$ then we have that $$\left|z_2\frac{z_1}{z_2}\right|=|z_1|\implies|z_2|\bigg|\frac{z_1}{z_2}\bigg|=|z_1|\implies \bigg|\frac{z_1}{z_2}\bigg|=\frac{|z_1|}{|z_2|}$$
