# Math Help - Complex Exponential Forms

1. ## Complex Exponential Forms

This is another homework problem:

Where do I begin? The problem states: Show that in (5.2) the average value of sin(mx)sin(nx) and of cos(mx)cos(nx), m does not equal n, are zero (over a period), by using the complex exponential forms for the sines and cosines as in (5.3).

I have attached the equations being referenced from the book. I really don't have a good idea where to start. I'm thinking I should start with Euler's identity but I don't know what to do here.

2. $sin(mx)= \frac{e^{imx}- e^{-imx}}{2i}$ and $cos(mx)= \frac{e^{imx}+ e^{imx}}{2}$. Write your functions in terms of those and integrate.