I found an inconsistency:
julia> -im * big(0.0-10.0im)
-10.0 - 0.0im
julia> -im * (0.0-10.0im)
-10.0 - 0.0im
julia> -im * ComplexDF64(0.0-10.0im) # has opposite imaginary sign
-10.0 + 0.0im
This causes the following to give different results:
julia> log( -im * (0.0-10.0im))
2.302585092994046 - 3.141592653589793im
julia> log(-im * ComplexDF64(0.0-10.0im))
2.30258509299404568401799145468437419 + 3.14159265358979323846264338327950588im