So i just had a "duh" moment with myself. Modern physics exam on Monday (I lied before about my exam schedule and I can't read a calendar, so I have this weekend to study for it), going over the first homework assignment which involved complex numbers and adding waves. I completely missed the identities my teacher gave us for complex numbers and sinusoidal functions, and as a result had no idea how to convert from either to the other lol. Now how you went through those transformations makes even more sense. Just thought I'd share my "Hey I got it but I'm an idiot" moment, lol
Now I get to move on to studying Fourier Transforms, Interference, and Michelson Interferometers.