One of the main drawbacks of Fourier domain optical coherence tomography (FDOCT) is the limited measurement depth range. Phase shifting techniques allow reconstructing the complex sample signal resulting in a doubled depth range. In current complex FDOCT realizations the phase shift is introduced via a reference path length modulation, which causes chromatic phase errors especially if broad bandwidth light sources are employed. With acousto-optic frequency shifters in the reference and sample arm, and the detector being locked to the resulting beating frequency, the signal is quadrature detected at high speed. The beating signal frequency is the same for all wavelengths allowing for achromatic complex reconstruction. With a Ti:Sapphire laser at 800nm and spectral width of 130nm, a heterodyne complex FDOCT system is realized with 20kHz line rate and an axial resolution of 4µm.