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Math Help - Complex Exponential Forms

  1. #1
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    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.
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  2. #2
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    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.
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