Hi guys, I lurk here often for general advice, but now I need help with a specific concept. Ok, so I started a classical and quantum waves class this semester. We are beginning with classical waves and using Vibrations and Waves by A P French as the text. So in the second chapter he discusses wave superposition and describing the motion of two waves added together with a single equation. In the book, he explains most things geometrical, using the complex vector and complex exponential notation for the wave. He draws both waves and uses law of sines and law of cosines to determine the combined amplitude/frequency/phase angle. One of the homework problems is then: Express z=sinwt + coswt in the form z=Re[Ae^i(wt+a)] I was able to accomplish this geometrically with little difficulty and correctly got the answer to be A=root 2 and a=-pi/4. However, my professor said that I should not necessarily rely on the geometry and should be able to get the answer mathematically using the complex exponential form. I have tried it this way and do not really understand how to go about it. Do I represent sinwt as -iAe^i(wt+a) or possibly as Ae^i(pi/2-wt-a). Honestly, that particular problem is not that important. I just want to gain insight on how to find the superposition of waves by manipulating different complex exponentials.