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