Question

which equation demonstrates the multiplicative identity property

Answer 1

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

Further explanation

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 1

The multiplicative identity property states that any number multiplied by 1 will produce an original number.

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

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Keywords: Multiplicative Identity property, integers

Answer 2

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.

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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.