1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nadya [2.5K]
3 years ago
6

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

olynomials?
Mathematics
2 answers:
ozzi3 years ago
8 0
By using Associative, Commutative, and Distributive Properties in performing operations on complex numbers and polynomials, you would be able to simplify correctly and simply. To combine complex numbers, you must distribute any coefficients in front of the parentheses. Then identify and<span>combine like terms by combining the real number parts and the imaginary number parts separately.</span>
Elena-2011 [213]3 years ago
4 0

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}\times [Z_{2}+Z_{3}]=Z_{1} \times Z_{2}+Z_{1}\times 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.

You might be interested in
Find the volume of the cylinder.Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and round
AveGali [126]

complete question:

Find the volume of the cylinder.

Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth.

Radius = 4 and height = 8.

Answer:

volume of a cylinder ≈ 402.30  unit cube

Step-by-step explanation:

The question you to find the volume of a cylinder with a height of 8 and radius of 4. The volume of a cylinder can be represented below

volume of a cylinder =  πr²h

where

h = height

r = radius

h = 8

r = 4

volume of a cylinder =  πr²h

volume of a cylinder =  π × 4² × 8

volume of a cylinder =  π × 16 × 8

volume of a cylinder = 128  π

volume of a cylinder =  128 × 3.143

volume of a cylinder = 402.304

volume of a cylinder ≈ 402.30  unit cube

6 0
3 years ago
Math:
Dahasolnce [82]

Answer:

a) x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}, x_{2} = \frac{5\pi}{6}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}, b) x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}, x_{2} = \frac{5\pi}{3}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}

Step-by-step explanation:

a) The equation must be rearranged into a form with one fundamental trigonometric function first:

\sqrt{3}\cdot \csc x - 2 = 0

\sqrt{3} \cdot \left(\frac{1}{\sin x} \right) - 2 = 0

\sqrt{3} - 2\cdot \sin x = 0

\sin x = \frac{\sqrt{3}}{2}

x = \sin^{-1} \frac{\sqrt{3}}{2}

Value of x is contained in the following sets of solutions:

x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}

x_{2} = \frac{5\pi}{6}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}

b) The equation must be simplified first:

\cos x + 1 = - \cos x

2\cdot \cos x = -1

\cos x = -\frac{1}{2}

x = \cos^{-1} \left(-\frac{1}{2} \right)

Value of x is contained in the following sets of solutions:

x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}

x_{2} = \frac{5\pi}{3}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}

7 0
3 years ago
15. A restaurant has one type of milk that has 2% fat and another that has 7% fat. how many quarts of each type does the restaur
krek1111 [17]
<span>B. 16 quarts of the 2% milk and 24 quarts of the 7% milk First, let's create an equation to solve. x = quarts of 2% milk (40-x) = quarts of 7% milk So we have the equation x*2 + (40-x)*7 = 40*5 Now to solve for x x*2 + (40-x)*7 = 40*5 x*2 + 7*40 - 7*x = 40*5 x*2 - 7*x = 40*5 - 7*40 -5*x = - 2*40 x = 2*8 x = 16 So we need 16 quarts of 2% milk and 40-16 = 24 quarts of 7%, which matches option "B".</span>
5 0
3 years ago
4,275.50= 391/2 of ____
murzikaleks [220]

Answer:

The required value for the blank is 21.8696

Step-by-step explanation:

Consider the provided information,

4,275.50= 391/2 of ____

Replace blank with x.

4,275.50 = 391/2 of x

Use sign of multiplication for "of".

4,275.50 = \frac{391}{2} \times x

Solve the above expression for x.

x=\frac{4,275.50\times 2}{391}

x=21.8696

Thus, the required value for the blank is 21.8696

8 0
3 years ago
Jawan made a table to figure out how much he earns at his job (image below)
slega [8]

Answer:

Th rule here is that every week he works 6 more hours and in those six hours he adds $54 to the original price

Step-by-step explanation:

Answer for question B:

324

3 0
3 years ago
Read 2 more answers
Other questions:
  • Does anyone know how to do this?
    12·1 answer
  • What is equivalent to y=(x+3)2+53
    13·2 answers
  • Segments proofs. B is the midpoint of AC Prove 2bc=AB
    9·1 answer
  • Please answer the question from the attachment.
    14·1 answer
  • Brian is riding his bike. He biked a distance of 14 miles at a rate of 14 miles per hour. Rearrange the distance formula, d = rt
    10·2 answers
  • What percent is 2.5 of 40
    11·2 answers
  • A cylinder has a volume of 3201 cubic inches and a height of 5 inches.
    9·1 answer
  • A shape is made up of 8 right triangles of equal size. each right triangle has a base of 4cinches and a height of 15 inches. wha
    10·2 answers
  • Easy 10 points (question is down below, thank you.)
    7·1 answer
  • The dimensions of a rectangular prism are given in the net shown.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!