Answer with explanation:
Complex Numbers
For,any two or more complex numbers , [tex]Z_{1},Z_{2},Z_{3}[/tex],
1. Commutative Property
[tex]Z_{1}+Z_{2}=Z_{2}+Z_{1}[/tex]
2. Associative Property
[tex]Z_{1}+(Z_{2}+Z_{3})=(Z_{1}+Z_{2})+Z_{3},[/tex]
3.Distributive Property
[tex]Z_{1}\times [Z_{2}+Z_{3}]=Z_{1} \times Z_{2}+Z_{1}\times Z_{3}[/tex]
Hence Complex number follows ,Associative, Commutative, and Distributive Property.
Polynomials ⇒
P=a x +b, Q=c x²+ t x+d, R=m x³+ n x²+ r x+s
1. Commutative Property
P+Q=a x+b+c x²+ t x+d
=c x²+ t x+d+a x+b
=Q+P
2. Associative Property
(P+Q)+R=(a x+b+c x²+ t x+d)+m x³+ n x²+ r x+s
=a x+b+(c x²+ t x+d+m x³+ n x²+ r x+s)
= P + (Q+R)
3.Distributive Property
P×(Q+R)
(ax+b)×[c x²+ t x+d+m x³+ n x²+ r x+s]
=(ax+b)×[c x²+ t x+d]+(ax+b)[m x³+ n x²+ r x+s]
=P ×Q+P×R
Hence Polynomial follows ,Associative, Commutative, and Distributive Property.
