If I have a complex fraction, say $$z=\frac{a+bi}{c+di}$$, how can I find the phase angle of this? Could I just calculate it using $$\arctan(\frac{b}{a})-\arctan(\frac{d}{c})?$$
For example, my textbook says that for the fraction $$z=\frac{j\omega}{1+j\omega},$$ the phase angle should be $$\arctan(\frac{1}{\omega}).$$ I'm not really understanding what method/identities they're using to arrive at this answer.Is there a standard way to find the phase angle of a complex fraction?