This study investigates classical differential geometry of isotropic curves in the complex space C-3. First, we deal with spherical images of isotropic curves, and then obtain some results regarding these curves. Therefore, we continue to study these spherical indicatrices as Darboux curves and Bertrand mates. Also, we examine isotropic slant helices in C-3. Additionally, we show that the vectors of isotropic curves and their pseudo-curvatures satisfy a vectorial differential equation of the second order with variable coefficients. We study this differential equation under some special cases. Finally, we give the conditions for an isotropic curve to be Darboux helix in C-3. Next, we define the constant breadth of isotropic curves and express some characterizations of these curves in terms of E. Cartan equations in C-3. (C) 2016 Elsevier Inc. All rights reserved.