In this article, we describe the results of a case study examining the development of two undergraduate students’ geometric reasoning about the derivative of a complex-valued function with the aid of The Geometer’s Sketchpad (GSP). Initially, our participants saw it in terms of the slope of the tangent line. Without the aid of GSP, they could describe the rotation and dilation aspect of the derivative for linear complex-valued functions, but were unable to generalize this perception to non-linear ones. Participants’ use of GSP assisted with exploring function behavior, generalizing how for non-linear complex-valued functions the derivative describes the rotation and dilation of an image with respect to its pre-image, and recognizing that the derivative is a local property.