This caught me by surprise:
julia> x = randn(5); P = plan_rfft(x);
julia> eltype(P)
Float64
julia> P * x
3-element Vector{ComplexF64}:
 -0.3514539021978911 + 0.0im
 -0.8023047651675712 + 1.243731722698685im
  2.8759555200391196 - 2.679171588261927imIf a "plan" is in some sense analogous to a matrix the eltype should be type of the output, in this case ComplexF64.