Your task is both a challenge and an opportunity: they will be unfamiliar with complex numbers, but perhaps you could motivate the utility of complex numbers.
I might try to introduce them to the computation of a Julia set, at first entirely computationally,
showing them how $z$ grows under repeated computation of `znew = zold² + c`

, all in terms
of coordinates and distance from the origin (without mentioning complex numbers). They need not know any programming
language to understand a simple iterative loop.
Once they see how some starting points $z$ scoot off to infinity, and others hang around the origin,
they can appreciate it would be natural to color each point according to its scooting-to-$\infty$ speed.
And then they could understand how to make a Julia set:

_{(Image from cgtutor)}

With this understanding secured, you might be able to introduce complex numbers.

For motivating applications, you could easily connect to the use of fractals in
computer graphics in movies (*Lord of the Rings*; *The Hobbit*, etc.):

_{(Image from LifeInWireframe)}

youin advance! It was just such a lecture that got me interested in mathematics, and now I am in graduate school. $\endgroup$ – Robert Haraway Apr 20 '13 at 0:44