Exercise 3.  Find all the values of z for which each equation holds.  

3 (a).  [Graphics:Images/ComplexFunLogarithmModHome_gr_248.gif].  

Solution 3 (a).

See text and/or instructor's solution manual.

Answer.   [Graphics:../Images/ComplexFunLogarithmModHome_gr_249.gif].

Solution.   

                    [Graphics:../Images/ComplexFunLogarithmModHome_gr_250.gif]   

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunLogarithmModHome_gr_251.gif]

[Graphics:../Images/ComplexFunLogarithmModHome_gr_252.gif]


[Graphics:../Images/ComplexFunLogarithmModHome_gr_253.gif]

[Graphics:../Images/ComplexFunLogarithmModHome_gr_254.gif]


[Graphics:../Images/ComplexFunLogarithmModHome_gr_255.gif]

[Graphics:../Images/ComplexFunLogarithmModHome_gr_256.gif]

                         [Graphics:../Images/ComplexFunLogarithmModHome_gr_257.gif]          [Graphics:../Images/ComplexFunLogarithmModHome_gr_258.gif]

                                        The value   [Graphics:../Images/ComplexFunLogarithmModHome_gr_259.gif]   which solves the equation   [Graphics:../Images/ComplexFunLogarithmModHome_gr_260.gif].  
                                        This mapping is given by the function  [Graphics:../Images/ComplexFunLogarithmModHome_gr_261.gif].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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