My suggestion -- assuming they have not yet taken a class on complex analysis -- would be to talk about [Eulers formula][1]  and [De Moivre's formula][2], along with the complex representations of the most common trigonometric functions. Perhaps, if there is time left, power series and the [Cauchy product][3] could be touched upon.

This could help the students to understand better how some trigonometric identities can be derived, which is usually not explained in detail until a first course on complex analysis. 

Each of the topics is simple enough to introduce in a very short amount of time, so there would probably be time left to show some cool applications.


  [1]: http://en.wikipedia.org/wiki/Eulers_formula
  [2]: http://en.wikipedia.org/wiki/De_Moivre%2527s_formula
  [3]: http://en.wikipedia.org/wiki/Cauchy_product