I have found an interesting bug (or at least I can't explain this):
f1[x_] := Sin[2*Pi*x/10] + I*Cos[2*Pi*x/20]
f2[x_] := Abs[f1[x]]
f3[x_] := f2'[x]
Output looks like:
(-(1/40) I (-1 + Sqrt) \[Pi] +
1/20 (1 + Sqrt) \[Pi]) Derivative[Abs][
Sqrt[5/8 - Sqrt/8] + I Sqrt[5/8 + Sqrt/8]]
So, initially I had a complex function (f1), then turned it into a real value function (f2), then attempted to get a derivative - voila! - imaginary unit is back! How?!!!
Just in case - attached is a screenshot.
Attachment: glitch.JPG, URL: ,