Matthew' solution is correct but in some way incomplete: since two eigenvalues are complex (and complex conjugate) there are two forms of solutions: a complex form and he found only the complex form; Iven and Victor found both. despite Victor' solution looks different it is not: in fact he got the same eigenvector albeit multiplied by factor $-2i$ (which be also an eigenvector) and this is the source of "discrepancy".
