Example 5.11.  The values of  [Graphics:Images/ComplexFunTrigInverseMod_gr_126.gif]  are given by  

            [Graphics:Images/ComplexFunTrigInverseMod_gr_127.gif].  

Using straightforward techniques, we simplify this equation and obtain  

[Graphics:Images/ComplexFunTrigInverseMod_gr_128.gif]

where n is an integer.  We observe that  

            [Graphics:Images/ComplexFunTrigInverseMod_gr_129.gif]
and then write

            [Graphics:Images/ComplexFunTrigInverseMod_gr_130.gif],   where n is an integer.

Explore Solution 5.11.

Use the formulas in the text to get the answers.

[Graphics:../Images/ComplexFunTrigInverseMod_gr_131.gif]




[Graphics:../Images/ComplexFunTrigInverseMod_gr_132.gif]

 

 

We can check out the principal values.

[Graphics:../Images/ComplexFunTrigInverseMod_gr_133.gif]




[Graphics:../Images/ComplexFunTrigInverseMod_gr_134.gif]

 

 

[Graphics:../Images/ComplexFunTrigInverseMod_gr_135.gif]




[Graphics:../Images/ComplexFunTrigInverseMod_gr_136.gif]