$$\dfrac {j \,n\pi}{(1+j \, n \pi)} \left(\dfrac {2}{n\pi}\right) (1 - \cos(n \pi))\angle -90° = \dfrac {2(1-\cos(nπ))}{(\sqrt{1+n^2 \pi^2}\angle (90°-\tan^{-1}(n \pi)-90°)}$$
Complex expression more legible
How can one simply get the magnitude and phase angle from the expression on the left hand side. I am having trouble separating the real and imaginary components. When I am able to do this they are always overwhelming expressions whose magnitude is difficult to get.