Fsc Part 1 Mathematics (Complete Solution)
Q3
Verify the distributive law of complex numbers.
(a,b)[(c,d)+(e,f)] = (a,b)(c,d)+(a,b)(e,f)
SOLUTION:
L.H.S=(a,b)[(c,d)+(e,f)]
=(a,b)(c+e,d+f)
=[a(c+e)-b(d+f),a(d+f) +b(c+e)]
=[(ac+ae-bd-bf),(ad+af+bc+be)]
=[(ac-bd)+(ae-bf),(ad+bc)+(af+be)]
=(ac-bd,ad+bc)+(ae-bf,af+be)
=(a,b)(c,d)+(a,b)(e,f)
=R.H.S