Fourier domain optical coherence tomography (FDOCT) is a high speed imaging technique with high axial resolution in the micro-meter-scale range combined with a high sensitivity allowing to probe 3D volumes of weakly back- scattering biological tissues in-vivo. Phase shifting techniques allow the reconstruction of the full complex sample signal which results in an additional suppression of unwanted auto-correlated distortion as well as an extended depth range. Current complex FDOCT realizations introduce the phase shift via reference path length modulation causing chromatic phase errors especially if broad bandwidth light sources are employed. Broad optical bandwidth is necessary for ultrahigh resolution OCT systems. By frequency shifting the light fields with acousto-optic frequency shifters in the reference and sample arm respectively, a phase-resolved signal at high speed can be registered. Therefore the reference arm does not rely on arm length changes or delays. The beating signal generated this way shows high phase stability. The phase of this beating signal is not wavelength-dependent, as the frequency shift applied is the same for all wavelengths. With a Ti:Sapphire laser at 800nm and a spectral width of 130nm a high speed complex FDOCT system is realized with an axial resolution of 4µm.