In this paper we investigate a class of complex Finsler metrics of Randers type defined by \(F(z,{\mu}) = {\alpha}(z,{\mu}) + |{\beta}(z,{\mu})|\) where \({\alpha}(z,{\mu}) = \sqrt{a_{\overline{ij}}{\mu}^i{\overline{\mu}}^j}\) is a Hermitian norm induced by a positive-definite Hermitian metric and \({\beta}(z,{\mu}) = {\frac{e}{m}}A_i(z){\mu}^i\) is a complex 1-form. Motivated by the analogies with electromagnetic interactions we refer to these as electro-complex  Randers metric and we explore conformal deformations of such spaces.