16 Mr Greenhill, Complex Multiplication [Oct. 29, 



+ c 2 {- 60 - 40 Jb + 40 J5 + 20 JTE- 1344 - 768 73 



+ 576 75 + 336 JlE} 

 + c 3 {- 12 - 8 73 + 8 J5 + 4 v/l5 + 28 + 16 73 - 12 75 - 7 Jl5) 

 = _ 1355 _ 766 JS + 584 75 + 340 7l5 



+ c (892 + 504 JS - 368 J 5 - 218 7l5} 



-c 2 {1404 + 808^3 - 616 s/5- 356 715} 



+ c 3 {16 + 8 S - 4 J 5 - 3 715} 

 = - 1355 - 776 S + 584 75 + 340 J 15 



+ c {892 + 504 73 - 368 J 5 - 218 7l5} 



-c 2 {17 + 8^3} 



= - 1355 - 776 S + 584 J 5 + 340 7l5} 

 + c {32 + 8 ^3 + 4 75 - 3 ^15} 



= - 1355 - 776 73 + 584 75 + 340 Jl5 



+ 1355 + 776 73 - 584 75 - 340 7l5 

 = 0. 



Therefore the equations for a and ft are consistent, and therefore 

 1+2/ can be put into the required form. 



Thus . 1 +S = ^±|M, 



where P = i — 1 + 2 J2c -c— ic, 



D = (i- 1 + 72c) {(ic - x 2 ) 2 - 2x 2 J^ic (1 - ic) } 



+ (i-l- 72c) (ic - x 2 ) (1 - J^icfx, 



and a and /3 are given by the equations 



a/3 = — ic 



„ . „ i — 1 — 2 72c — c — ic .- i — - N „ 

 2 (a + /3) = -- -7= (1 -7-ic 2 . 



