I am usually more comfortable working with sines and cosines. However, its often cleaner and more efficient to work with exponentials.
Is there a reason other then preference, to use one over the other?
EDIT: Thinking more on this, Exp Fourier series allows the spectra to be expanded into negative frequency. But in the end, isnt this the same information?
Speaking as an EE, imaginary exponentials are generally easier to manipulate then their trigonometric counterparts since they essentially let you get a polynomial out of your sin/cos function.
For example if I gave you $$ \cos \Bigg(n_1\omega t+\theta_1\Bigg)\cos\Bigg(n_2\omega t+\theta_2\Bigg) $$
You can imagine trying to do any kind of algebra with that. Using exponentials we can write it in a simpler form.
$$ \Bigg[\mathrm e^{\theta_1}\mathrm e^{jn_1\omega t}+\mathrm e^{\theta_1}\mathrm e^{-jn_1\omega t} \Bigg] \Bigg[\mathrm e^{\theta_2}\mathrm e^{jn_2\omega t}+\mathrm e^{\theta_2}\mathrm e^{-jn_2\omega t} \Bigg] $$
Do some math and you get him down to $$ \Bigg[\mathrm e^{\theta_1\theta_2}\mathrm e^{j\omega t(n_1+n_2)}+\mathrm e^{\theta_1\theta_2}\mathrm e^{-j\omega t(n_1+n_2)} \Bigg]+\Bigg[\mathrm e^{\theta_1\theta_2}\mathrm e^{j\omega t(n_2-n_1)}+\mathrm e^{\theta_1\theta_2}\mathrm e^{-j\omega t(n_2-n_1)} \Bigg] $$
And simplify to $$ \cos \Bigg[(n_1+n_2)\omega t + \theta_1\theta_2) \Bigg]+\cos \Bigg[(n_2-n_1)\omega t + \theta_1\theta_2) \Bigg] $$
That looks much nicer doesn't it?