Explanation for complex term in Solve[ ] output?

Dear Madame / Sir,
I have the following question (may be easy for you but unfortunately not for me).
Where the 2πic (where c is belonging to Z) is coming from as imaginary part of the solution of an exponential equation ? Attached is the .nb.
I know even manually how to solve for the real part but not for the imaginary one.

Thanx !

imaginary part of an exponential equation.nb (3.35 KB)