Exercise 1.  Find a parametrization of the line that  

1 (a).  joins the origin  [Graphics:Images/ComplexPlaneTopologyModHome_gr_1.gif]  to the point  [Graphics:Images/ComplexPlaneTopologyModHome_gr_2.gif].  

Solution 1 (a).

See text and/or instructor's solution manual.

        [Graphics:../Images/ComplexPlaneTopologyModHome_gr_3.gif]

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexPlaneTopologyModHome_gr_4.gif]

        

         [Graphics:../Images/ComplexPlaneTopologyModHome_gr_5.gif]

  

        The line  [Graphics:../Images/ComplexPlaneTopologyModHome_gr_6.gif],   and  

        the initial point is  [Graphics:../Images/ComplexPlaneTopologyModHome_gr_7.gif]  and the terminal point is  [Graphics:../Images/ComplexPlaneTopologyModHome_gr_8.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2008 John H. Mathews, Russell W. Howell