Abstract: The electroweak production and subsequent decay of single top quarks is determined by the properties of the Wtb vertex. This vertex can be described by the complex parameters of an effective Lagrangian. An analysis of angular distributions of the decay products of single top quarks produced in the t-channel constrains these parameters simultaneously. The analysis described in this paper uses 4.6 fb(-1) of proton-proton collision data at root s = 7 TeV collected with the ATLAS detector at the LHC. Two parameters are measured simultaneously in this analysis. The fraction f(1) of decays containing transversely polarised W bosons is measured to be 0.37 +/- 0.07 (stat. circle plus syst.). The phase delta_ between amplitudes for transversely and longitudinally polarised W bosons recoiling against lefthanded b-quarks is measured to be -0.014 pi +/- 0.036 pi (stat. circle plus syst.). The correlation in the measurement of these parameters is 0.15. These values result in two-dimensional limits at the 95% confidence level on the ratio of the complex coupling parameters g(R) and V-L, yielding R-e[g(R)/V-L] is an element of [-0.36; 0.10] and Im[g(R)/V-L] is an element of [-0.17; 0.23] with a correlation of 0.11. The results are in good agreement with the predictions of the Standard Model.