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nikdorinn [45]
3 years ago
9

Which equation demonstrates the multiplicative identity property

Mathematics
2 answers:
Sveta_85 [38]3 years ago
6 0

The option B \boxed{\left( { - 3 + 5i} \right)\left( 1 \right) =  - 3 + 5i} demonstrates the multiplicative identity.

Further explanation:  

The equation that satisfies the condition of multiplicative identity for the complex number can be represented as,

a \times b = a = b \times a  

Here, a is the multiplicative identity and it can be observed that the multiplicative identity would be 1 where b is the complex number.

The equation that satisfies the condition of additive identity for the complex number can be represented as,

a + b = a = b + a  

Here,  is the additive identity and it can be observed that the additive identity would be 0 where b is the complex number.

Step by step explanation:

We have to determine the multiplicative identity property among all the options.

Option A:  \left( { - 3 + 5i} \right) + 0 =  - 3 + 5i

It can be observed that the equation \left( { - 3 + 5i} \right) + 0 =  - 3 + 5i satisfies the condition of the additive identity as 0 is the additive identity.

Therefore, the option A is not correct option.

Option B: \left( { - 3 + 5i} \right)\left( 1 \right) =  - 3 + 5i

It can be observed that the equation \left( { - 3 + 5i} \right)\left( 1 \right) =  - 3 + 5i satisfies the condition of the multiplicative identity as 1 is the multiplicative identity.

Therefore, the option B is correct option.

Option C: \left( { - 3 + 5i} \right)\left( { - 3 + 5i} \right) =  - 16 - 30i

It can be observed that the equation \left( { - 3 + 5i} \right)\left( { - 3 + 5i} \right) =  - 16 - 30i does not satisfy the condition of the multiplicative identity as well as additive identity.  

Therefore, the option C is not correct option.

Option D:  \left( { - 3 + 5i} \right)\left( {3 - 5i} \right) = 16 + 30i

It can be observed that the equation \left( { - 3 + 5i} \right)\left( {3 - 5i} \right) = 16 + 30i does not satisfy the condition of the multiplicative identity as well as additive identity.  

It shows the product of one complex number with its conjugate.

Therefore, the option D is not correct option.

Result:  

Therefore, there is only one option that is option B \left( { - 3 + 5i} \right)\left( 1 \right) =  - 3 + 5i demonstrates the multiplicative identity.

Learn more:  

  1. Learn more about the function is graphed below brainly.com/question/9590016
  2. Learn more about the symmetry for a function brainly.com/question/1286775
  3. Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Complex number

Keywords: Multiplication, multiplicative identity, complex number, equation, additive identity, condition, conjugate, arithmetic properties, sum, operation, real numbers.

nignag [31]3 years ago
4 0

<em>Equation b) (-3 + 5i) (1) = -3 + 5i  demonstrates the multiplicative identity property </em>

<h3>Further explanation</h3>

There are several properties in integer multiplication operations

  • 1. closed property

Multiplication between integers will produce integers too

  • 2. commutative property

a x b = b x a

  • 3. associative property

ax (bxc) = (axb) xc

  • 4. identity

ax1 = 1 x a = a

  • 5. distributive  property

* addition

ax (b + c) = axb + axc

* substraction

ax (b-c) = axb - axc

The Multiplicative Identity is <u><em>1 </em></u>

<u><em>The multiplicative identity property states that any number multiplied by 1 will produce an original number. </em></u>

We complete the answer choices available from the problem above:

a) (- 3 + 5i) + 0 = -3 + 5i

O is an identity in the sum operation, the statement is false

b) (-3 + 5i) (1) = -3 + 5i

1 is a Multiplicative Identity of multiplication, so the statement is true

c) (-3 + 5i) (-3 + 5i) = -16-30i

d) (-3 + 5i) (-3 + 5i) = 16 + 30i

choice c and is a multiplication factor, so the statement is false

<h3>Learn more </h3>

the substitution method

brainly.com/question/11705106

brainly.com/question/7162056

The work of a student to solve a set of equations

brainly.com/question/10589573

Keywords: Multiplicative Identity property, integers

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