Q^IO ON THE ALGORITHM OF IMAGINARY QUANTITIES. 



' 3 . » 



3 3 



+ V'"(— 2— 11 V'— !)*« 

 Again 



(B)../ /— i-f ^ vz-s + /— f ~~ t v — syzz 



^ — __ 3 : ^ 



V{-i-:iv/-3)' 



> Thus far we have proceeded step by step the same in both 

 examples, and let us still conthiue the same parallelism of 

 operation at full length thus : 



4 1 1 V-- 1 ? ^j^g square of (— 2 + 11 v'— l) 

 + 11\^— M 



4 _ 44 a/— 1— 121 =— 117 — 44v/— 1 = (— 2 + 11 y'— 1)* 



— 2+11 V— J? the prod, of (—2 1- 11 V-- 1) (^2— llv/— 1) 



— 2—11 -/— li 



4 +121 '/— 1 = 125 



— 2 ^ V V— 1 ? the souare of (-. 2 — 11 >/— 1) 



— 2 — 1 1 v/~ 1 S 



4+44 V-^ I ~ 121 - — 1 17 + 44 a/— 1 = ( — ^ — 1 1 '/— 1)* 

 and consequently our square (A) becomes 

 |/^_- 117 — 44 a/— 1 + 2 j/l25 + V — 1'7 + 44 V— 1 3 



/^ 117 :.- 44 V— 1 + 10 + V^— H7 + 44 V'— 1 



Again, 



