The zeros of the partition function in the one-dimensional q-state Potts model with arbitrary and continuous q>or=0 have been studied using a transfer matrix. The location of zeros and the Yang-Lee edge singularity have been analysed, and two different regimes, corresponding to q>1 and q>1, have been observed. A duality relation has also been derived, which relates the zeros in the complex field plane to those in the complex temperature plane.