Exploration

[Graphics:../Images/CauchyRiemannMod_gr_20.gif]

[Graphics:../Images/CauchyRiemannMod_gr_21.gif]

[Graphics:../Images/CauchyRiemannMod_gr_22.gif]

[Graphics:../Images/CauchyRiemannMod_gr_23.gif]

[Graphics:../Images/CauchyRiemannMod_gr_24.gif]

We will need to zoom in closer to the point [Graphics:../Images/CauchyRiemannMod_gr_25.gif].

[Graphics:../Images/CauchyRiemannMod_gr_26.gif]

[Graphics:../Images/CauchyRiemannMod_gr_27.gif]

[Graphics:../Images/CauchyRiemannMod_gr_28.gif]

[Graphics:../Images/CauchyRiemannMod_gr_29.gif]

[Graphics:../Images/CauchyRiemannMod_gr_30.gif]

We will need to zoom in closer to the point [Graphics:../Images/CauchyRiemannMod_gr_31.gif].

[Graphics:../Images/CauchyRiemannMod_gr_32.gif]

[Graphics:../Images/CauchyRiemannMod_gr_33.gif]

[Graphics:../Images/CauchyRiemannMod_gr_34.gif]

[Graphics:../Images/CauchyRiemannMod_gr_35.gif]

[Graphics:../Images/CauchyRiemannMod_gr_36.gif]

Now we are sufficiently close to see the image points are  [Graphics:../Images/CauchyRiemannMod_gr_37.gif],  [Graphics:../Images/CauchyRiemannMod_gr_38.gif],  [Graphics:../Images/CauchyRiemannMod_gr_39.gif],  and  [Graphics:../Images/CauchyRiemannMod_gr_40.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell