Elementary Differential Equations, Complex Analysis, or any other course where functions of a complex variable are considered.
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In Elementary Differential Equations, students encounter the connections between the complex exponential function and the trigonometric functions. I wrote this mathlet so the students could experiment and see these connections, rather than just considering Taylor series. The students found the graphs stimulating (and occasionally pretty). I've since used the mathlet in Complex Analysis to help enrich students understanding of branch cuts and the argument principle as well.
AVAILABILITY OF CODE:
The mathlet page includes documentation and source code for the mathlet (including a complex function parser). This code is copyrighted, but may be adapted as desired and used freely for non-commercial purposes provided the original source is acknowledged and the author is informed.
Open Complex Function Grapher in a new window.