Transport, photoluminescence, THz transmission, and optically detected cyclotron resonance studies were carried out on samples with a single modulation-doped CdTe/Cd _1-xMg _xTe quantum well. THz experiments were performed at liquid helium temperatures for photon energies between about 0.5 meV and 3.5 meV. An effective mass of electron was determined to be (0.1020±0.0003)m ₀. Observed photoluminescence and optically detected cyclotron resonance spectra cannot be explained within the simple model of Landau quantization of parabolic bands.