Trignometric Polynomial complex form

  1. Hi,
    I'm trying to learn Fourier transforms by myself. I'm a bit confused about how the trignometric polynomial complex form was derived. I'm refering to this:

    http://en.wikipedia.org/wiki/Trigonometric_polynomial

    Now, I haven't taken complex analysis so I only know the basics. I used Euler's formula and got that far but I'm not sure what to do next.

    Thanks
     
  2. jcsd
  3. micromass

    micromass 19,679
    Staff Emeritus
    Science Advisor
    Education Advisor

    Substitute

    [tex]\cos(nx)=\frac{e^{inx}+e^{-inx}}{2}, ~\sin(nx)=\frac{e^{inx}-e^{-inx}}{2i}[/tex]

    in the series and rearrange everything. This should give you the required form.
     
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