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