Here, we consider a function dealing with the conjugate of a given complex number.[br]Use the sliders or enter values for [math]a[/math] and [math]b[/math]. This will define the numbers [math]z_1[/math] and [math]z_2[/math] accordingly. (Notice that [math]z_1[/math] and [math]z_2[/math] are conjugates of one another!)[br][br]Consider the following cases: [br]1) When neither [math]a[/math] nor [math]b[/math] are equal to zero[br]2) When both values are nonzero[br]3) When one is zero, but the other is not[br][br]How does this affect our traced function? (Pay attention to the orientation, too!)[br][br]Using the input box for [math]f[/math], play around with different functions with respect to [math]z_1[/math] and [math]z_2[/math]. How does the shape look in comparison to the original function?[br][br]If time permits, adjust the sliders to allow for larger values and repeat the same investigations.

App designed by Mason Taylor,[br]edited by Dorothea Nguyen