Solution 1.

See text and/or instructor's solution manual.

Answer.   [Graphics:../Images/JoukowskiTransModHome_gr_2.gif],  

where   [Graphics:../Images/JoukowskiTransModHome_gr_3.gif]   is the multi-valued square root function.  

Solution.   The equation   [Graphics:../Images/JoukowskiTransModHome_gr_4.gif]   implies that   [Graphics:../Images/JoukowskiTransModHome_gr_5.gif].  

Use the quadratic formula and obtain   

                    [Graphics:../Images/JoukowskiTransModHome_gr_6.gif]  

Therefore,  

                    [Graphics:../Images/JoukowskiTransModHome_gr_7.gif].

where   [Graphics:../Images/JoukowskiTransModHome_gr_8.gif]   is the multi-valued square root function.  

 

We are done.   

 

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/JoukowskiTransModHome_gr_9.gif]

[Graphics:../Images/JoukowskiTransModHome_gr_10.gif]

Remark.  Sometimes we write this as   [Graphics:../Images/JoukowskiTransModHome_gr_11.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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