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.

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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.