Is it ever $i$ time? I am asking this question as a response to reading two different questions:
Is it ever Pi time?
and 
Are complex number real?
So I ask, is it ever $i$ time?  Could we arbitrarily define  time as following the imaginary line instead of the real one?  
(NOTE:  I have NO experience with complex numbers, so I apologize if this is a truly dumb question.  It just followed from my reading, and I want to test my understanding)

In the Wikipedia article titled Paul Émile Appell, we read that "He discovered a physical interpretation of the imaginary period of the doubly periodic function whose restriction to real arguments describes the motion of an ideal pendulum."
The interpretation is this: The real period is the real period.  The maximum deviation from vertical is $\theta$.  The imaginary period is what the period would be if that maximum deviation were $\pi - \theta$.
