julia> a = complex(ones(8),ones(8))
[1.0 + 1.0im,1.0 + 1.0im,1.0 + 1.0im,1.0 + 1.0im,1.0 + 1.0im,1.0 + 1.0im,1.0 + 1.0im,1.0 + 1.0im]

julia> dot(a,a)
0.0 + 16.0im

Answer should be 16. I guess we need to do conj() somewhere.