Example 5.1.  For any integer n, the points  [Graphics:Images/ComplexFunExponentialMod_gr_92.gif]  are mapped onto a single point  

            [Graphics:Images/ComplexFunExponentialMod_gr_93.gif]  

in the w plane, as indicated in Figure 5.1.

[Graphics:Images/ComplexFunExponentialMod_gr_94.gif]

Figure 5.1  The points [Graphics:Images/ComplexFunExponentialMod_gr_95.gif] in the z plane (i.e., the xy plane) and their image  [Graphics:Images/ComplexFunExponentialMod_gr_96.gif] in the w plane (i.e., the uv plane). Explore Solution 5.1.

Enter the formula for the points.

[Graphics:../Images/ComplexFunExponentialMod_gr_97.gif]




[Graphics:../Images/ComplexFunExponentialMod_gr_98.gif]

 

 

 

Here is another way to look at it.

[Graphics:../Images/ComplexFunExponentialMod_gr_99.gif]




[Graphics:../Images/ComplexFunExponentialMod_gr_100.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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