[dupuis] 



SYMBOLIC USE OF DEMOIVRE'S THEOREM 



169 



Then by elimination we obtain 



a"= I /;" pn 'hi 



//'-- 1 p„. 

 /y-" 1 



//'-« 



Vn-A 

 1 



Now let 6 = F+ V-\ and let a" = F" + F"". 

 Then since VV-' = 1, 



h- = V" + V-" + "C'l ( F"-- + F-" + ^) + "a ( T' "-' + F-" + + 



= rt" + "C'la"-- 4- "Ooa"-^- + . . . 

 Similarly 



Whence by substitution 



F" + V-" =! ( F4- V-'T "C, »a "C3 



(F+ F-0"-^ 1 



(F4- F-^"-^ 



(F+ v~'y-' 



Or 2 cos 116 ^ 



1 "-^Ci 

 1 



which expresses the required relation in the form of a matrix. 



