TrackedComplex types

[gszep]

want a TrackedComplex type so that I can efficiently differentiate through FFTW.fft and also opens up the possibility of teaching Tracker complex analysis, contour integrals etc.

[gszep]

the following works as expected

using Flux
z = param([1-im,1+im])
typeof(z) # TrackedArray{…,Array{Complex{Float64},1}}
eltype(z) # TrackedComplex{Complex{Float64}}

but tracking is lost on element-wise vector operations

julia> exp(z[1])
1.4686939399158851 - 2.2873552871788423im (tracked)

julia> exp.(real(z))
Tracked 2-element Array{Float64,1}:
 2.718281828459045
 2.718281828459045

julia> exp.(z) # tracking lost
2-element Array{Complex{Float64},1}:
 1.4686939399158851 - 2.2873552871788423im
 1.4686939399158851 + 2.2873552871788423im

might have something to do with the fact that we can't subtype concrete type
TrackedComplex{T<:Complex} <: Complex

[gszep]

exp.(z) # tracking works!