Example 2.5.  Express  [Graphics:Images/ComplexFunLinear_gr_79.gif]  in polar form.

Explore Solution 2.5.

Enter the function.

[Graphics:../Images/ComplexFunLinear_gr_82.gif]

[Graphics:../Images/ComplexFunLinear_gr_83.gif]

 

 

Aside.  We can let Mathematica plot the image of a region under the mapping w = f[z].

[Graphics:../Images/ComplexFunLinear_gr_84.gif]

[Graphics:../Images/ComplexFunLinear_gr_85.gif]

[Graphics:../Images/ComplexFunLinear_gr_86.gif]

[Graphics:../Images/ComplexFunLinear_gr_87.gif]

[Graphics:../Images/ComplexFunLinear_gr_88.gif]

 

 

 

 

[Graphics:../Images/ComplexFunLinear_gr_89.gif]

[Graphics:../Images/ComplexFunLinear_gr_90.gif]

[Graphics:../Images/ComplexFunLinear_gr_91.gif]

[Graphics:../Images/ComplexFunLinear_gr_92.gif]

[Graphics:../Images/ComplexFunLinear_gr_93.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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