I don't really know how to take the log of complex numbers, but I'll start off like this:
phi = 2 cos (log ((i^2))/5*i)
phi = 2 cos (log (1)/5i)
phi = 2 cos (log (i/5))
phi = 2 cos (log i  log 5)
I would suggest applying the compound angle formula for cosine at this point.
