I am struggling with understanding the phase contribution of each individual pole. Let's say we have a system (minimum-phase system if it makes a difference) and it has poles located at:

<a href="https://www.codecogs.com/eqnedit.php?latex=s_1=r\cdot&space;e^{\frac{\pi}{4}}&space;,&space;s_2=r\cdot&space;e^{\frac{5\pi}{4}}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?s_1=r\cdot&space;e^{\frac{\pi}{4}}&space;,&space;s_2=r\cdot&space;e^{\frac{5\pi}{4}}" title="s_1=r\cdot e^{\frac{\pi}{4}} , s_2=r\cdot e^{\frac{5\pi}{4}}" /></a>

and

<a href="https://www.codecogs.com/eqnedit.php?latex=r&space;=&space;0.9" target="_blank"><img src="https://latex.codecogs.com/gif.latex?r&space;=&space;0.9" title="r = 0.9" /></a>

What is the analytical relation between the phase contribution of these two complex poles?