Question

How can the Associative, Commutative, and Distributive Properties be applied when performing operations on complex numbers and polynomials?

Answer 1

Answer with explanation:

Complex Numbers

For,any two or more complex numbers ,
`Z_(1),Z_(2),Z_(3)`,

1. Commutative Property

`Z_(1)+Z_(2)=Z_(2)+Z_(1)`

2. Associative Property

`Z_(1)+(Z_(2)+Z_(3))=(Z_(1)+Z_(2))+Z_(3),`

3.Distributive Property

`Z_(1)* [Z_(2)+Z_(3)]=Z_(1) * Z_(2)+Z_(1)* Z_(3)`

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.