I teach Maths in Victoria, Australia. I am obliged to give my students a problem solving task that lasts about 6 to 7 hours. The theme of the task I want to run is on Complex Numbers. Students at this level have only gone as far De Moivre's Theorem, though they could handle Euler's Theorem comfortably. They can also do simple problems of locus in the Argand diagram and solve simple polynomial equations with real and complex coefficients.
I am wondering if anyone can think of a problem solving task pitched at the level indicated above that students could do over a six to seven hour period.
The task needs to be broken up into six to seven questions, each question with subsections and such that each question fills about 45 minutes. I note that Mr.Fanastic is Australian and therefore may have a working knowledge of the education system in Victoria. If you do have any ideas that might be useful, please email me at the email address in my profile.
I posted this thread here rather than in the High School section because the problem solving task required needs the insight of a mathematician as opposed to a teacher.
Hoping someone out there can help.