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 number operations that involve multiplication:

• 1. commutative

$\boxed{\bold{a\times b=b\times a}}$

• 2. associative

$\boxed{\bold{a\times (b\times c)=(a\times b)\times c}}$

• 3. closed

Multiplication between integers will produce integers too

• 4. distributive property

* addition

$\boxed{\bold{a\times(b+c)=a\times b+a\times c}}$

* substraction

$\boxed{\bold{a\times(b-c)=a\times b-a\times c}}$

• 5. identity

The multiplicative identity property is a multiplicative property in mathematics where each number multiplied by 1 will produce the original number or can be stated simply  :

"The product of any number and one is that number"

So The Multiplicative Identity is 1

can be stated in the formula:

$\large{\boxed{\bold{a\times 1=1\times a=a}}}$

From the available answer choices

• a) (- 3 + 5i) + 0 = -3 + 5i

this is an addition operation and not multiplication while O is an identity in the sum operation, so the statement is false

• b) (-3 + 5i) (1) = -3 + 5i

this is a multiplication operation and 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

Learn more

the substitution method

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The work of a student to solve a set of equations

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Keywords: Multiplicative Identity property, integers, equation

Answer 2

The equation $\boxed{a + b = a = b + a}$ 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, $a$ is the additive identity and it can be observed that the additive identity would be 0 where $b$ is the complex number.

Consider an example $\left( { - 3 + 5i} \right) + 0 = - 3 + 5i$.

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.

Consider an example $\left( { - 3 + 5i} \right)\left( 1 \right) = - 3 + 5i$.

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.

Here, $a{\text{ is }}\left( { - 3 + 5i} \right)$ by comparing the general equation $a \times b = a = b \times a$  

Therefore, the second example $\left( { - 3 + 5i} \right)\left( 1 \right) = - 3 + 5i$ demonstrates the multiplicative identity.

Thus, in general the equation $a + b = a = b + a$ 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: Arithmetic properties

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