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: <br /> ![Julia set][1]<br /> <sub>(Image from [cgtutor][2])</sub><br /> 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.): <br /> ![FractalMountain][3]<br /> <sub>(Image from [LifeInWireframe][4])</sub><br /> [1]: http://lodev.org/cgtutor/images/juliaset.gif [2]: http://lodev.org/cgtutor/juliamandelbrot.html [3]: https://2.bp.blogspot.com/_iLtwy6ZDGfw/TBdlz7GVzoI/AAAAAAAAABs/3aUogqFtYpI/s1600/cool2.jpg [4]: http://lifeinwireframe.blogspot.com/2010/06/f-irst-of-all-fractals-are-bloody-huge.html