Indeed. There were 18th century mathematicians like Gauss who realized the importance of the geometric nature of complex numbers, but it didn't become central to the subject until the 19th century. The appearance of imaginary numbers as formal square roots of negative numbers goes back to the mid 16th century. As for Cartesian coordinates, i^2 = -1 has an intrinsic, coordinate-free interpretation in terms that would be instantly recognizable to the ancient Greeks, but it's certainly true that this way of thinking wasn't at the basis of the discovery and initial development of complex numbers, and thinking of geometric operators as generalized numbers would have seemed pretty alien for most of the 19th century as well.