How can the associative, commutative, and distributive properties be applied when performing operations on complex numbers and polynomials?

Answer with explanation:

Complex Numbers

For,any two or more complex numbers , ,

1. Commutative Property

2. Associative Property

3.Distributive Property

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.