Is there a function to find the period of an arbitrary (possibly complex) function in Mathematica?
Answer
You can check out this one. I don't know how well it works
Periodic`PeriodicFunctionPeriod[E^(I 2 Pi t) + Cos[3/9 Pi t], t]
6
Perhaps you are also interested in the other functions in that context. Check
Names["Periodic`*"]
EDIT
As @Artes notes in the comments, in v10 there's a documented version of this function called FunctionPeriod
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