In order to make the technology fit the idea, we had to name x as X, y as Y, u' is the partial derivative of f with respect to x, and v' is the partial of f with respect to y for the complex number z=x+y*i.[br][br]Go ahead and move the sliders for X and Y. There are two distinct shapes that occur if you move each slider separately. One is a parabola and the other is a line. Why does this happen? Note that u and v are defined as follows: [br] [img]https://latex.codecogs.com/gif.latex?u%28x%2Cy%29%3D2*x-y[/img] and [img]https://latex.codecogs.com/gif.latex?v%28x%2Cy%29%3Dx+y%5E2[/img]