Exercise 20.  Many texts give an alternative definition for  [Graphics:Images/ComplexFunExponentialModHome_gr_643.gif],  starting with (5-1) as the definition for  [Graphics:Images/ComplexFunExponentialModHome_gr_644.gif].  

20 (b).  Show that the result in part (a) implies that  [Graphics:Images/ComplexFunExponentialModHome_gr_660.gif].

This means  [Graphics:Images/ComplexFunExponentialModHome_gr_661.gif]  is constant with respect to x, so  [Graphics:Images/ComplexFunExponentialModHome_gr_662.gif],  where [Graphics:Images/ComplexFunExponentialModHome_gr_663.gif] is a function of y alone.

Solution 20 (b).

See text and/or instructor's solution manual.

Solution.   From part (a)   [Graphics:../Images/ComplexFunExponentialModHome_gr_664.gif],  hence

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_665.gif]   

This means  [Graphics:../Images/ComplexFunExponentialModHome_gr_666.gif]  is constant with respect to x, so  [Graphics:../Images/ComplexFunExponentialModHome_gr_667.gif],  where [Graphics:../Images/ComplexFunExponentialModHome_gr_668.gif] is a function of y alone.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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