Uses of eulers equation in fourier series

[amaresh92]

greetings,

why do we use Euler equation that is e ^(jωt)=cos(ωt)+i sin(ωt) in Fourier series and what does it represent?
advanced thanks.

 

[uart]

In general for a real periodic function, the Fourier decomposition is composed of both a Sine series and a Cosine series, both having real coefficients. The complex Fourier series (of a real function) that you describe is a convenient way of combining both of these into a single series solution.

It also has the advantage that often both sets of coefficients can be found using just the one integral equation, as opposed to a separate one for each of the Sine and Cosine series.