Complex cells can be found in the primary visual cortex (V1), the secondary visual cortex (V2), and Brodmann area 19 (V3).
Like a simple cell, a complex cell will respond primarily to oriented edges and gratings, however it has a degree of spatial invariance. This means that its receptive field cannot be mapped into fixed excitatory and inhibitory zones. Rather, it will respond to patterns of light in a certain orientation within a large receptive field, regardless of the exact location. Some complex cells respond optimally only to movement in a certain direction.
These cells were discovered by Torsten Wiesel and David Hubel in the early 1960s. They refrained from reporting on the complex cells in (Hubel 1959) because they did not feel that they understood them well enough at the time. In Hubel and Wiesel (1962), they reported that complex cells were intermixed with simple cells and when excitatory and inhibitory regions could be established, the summation and mutual antagonism properties didn't hold.
The difference between the receptive fields and the characteristics of simple and complex cells is the hierarchical convergent nature of visual processing. Complex cells receive inputs from a number of simple cells. Their receptive field is therefore a summation and integration of the receptive fields of many input simple cells, although some input is directly received from the LGN.
Source: Wikipedia https://en.wikipedia.org/wiki/Complex_cell