Recall that [math]u[/math] and [math]v[/math] are defined as follows:[br][center][math]u\left(x,y\right)=2x-y[/math][br][math]v\left(x,y\right)=x+y^2[/math] [/center]In order to make the technology fit the idea, denote [math]x[/math] as [math]X[/math], [math]y[/math] as [math]Y[/math].[br]Let [math]u'[/math] represent the partial derivative of [math]f[/math] with respect to [math]x[/math], and let [math]v'[/math] represent the partial of [math]f[/math] with respect to [math]y[/math] for the complex number [math]z=x+yi[/math].[br][br]Go ahead and move the sliders for [math]X[/math] and [math]Y[/math]. There are two distinct shapes that occur if you move each slider separately. One is a parabola and the other is a line. [br][br]Make conjectures on why this is happening.