A theoretical study of the 0⁺ resonance states of the ¹²С nucleus is performed using the 3α cluster model. Various phenomenological potentials are used to characterize the interaction between alpha particles. The results from calculations with different potentials are compared. The Schrödinger equation, transformed by means of complex rotation, is solved numerically using the finite element technique in order to determine the resonance energies. A set of new broad resonances is found.