diff --git a/base/dft.jl b/base/dft.jl
index 700bbc68c2dec..f1072d2ae99e6 100644
--- a/base/dft.jl
+++ b/base/dft.jl
@@ -24,6 +24,7 @@ typealias FFTWFloat Union{Float32,Float64}
 fftwfloat(x) = _fftwfloat(float(x))
 _fftwfloat{T<:FFTWFloat}(::Type{T}) = T
 _fftwfloat(::Type{Float16}) = Float32
+_fftwfloat{T}(::Type{Complex{T}}) = Complex{_fftwfloat(T)}
 _fftwfloat{T}(::Type{T}) = error("type $T not supported")
 _fftwfloat{T}(x::T) = _fftwfloat(T)(x)
 
diff --git a/test/fft.jl b/test/fft.jl
index b30e05ff09a5a..376d7e5e32248 100644
--- a/test/fft.jl
+++ b/test/fft.jl
@@ -6,6 +6,8 @@ a = rand(8) + im*rand(8)
 @test norm(ifft(fft(a,1),1) - a) < 1e-8
 @test norm(ifft(fft(a,[1]),[1]) - a) < 1e-8
 @test norm(ifft(fft(a,(1,)),(1,)) - a) < 1e-8
+a = rand(-10:10, 8) + im*rand(-10:10, 8)
+@test norm(ifft(fft(a)) - a) < 1e-8
 
 m4 = [16.    2     3    13;
     5    11    10     8;