Question

Which equation demonstrates the multiplicative identity property?

• A. $(-3+5i)+0=-3+5i$
• B. $(-3+5i)\left(1\right)=-3+5i$
• C. $(-3+5i)(-3+5i)=-16-30i$
• D. $(-3+5i)(3-5i)=16+30i$

Answer 1

The correct option is B

$(-3+5i)\left(1\right)=-3+5i$

Explanation For The Correct Option:

Option$\left(B\right)$:

The given expression

$(-3+5i)\left(1\right)=-3+5i$

We know a number $x$ is called multiplicative identity if $\forall a,a·x=a$

Here we can see that $1$ is an identity element because we get same expression after multiplication with it.

Hence, this equation demonstrates the multiplicative identity property.

Explanation For incorrect Options:

Option(A):

The given expression

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

Here $0$ is an additive identity.

Therefore, this equation demonstrates the additive identity property.

Hence, it is an incorrect option.

Option(C):

The given expression

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

It is nothing but square of a complex number.

So, It doesn't demonstrate any identity.

Hence, it is an incorrect option.

Option(D):

The given expression

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

This is also just a multiplication of two complex numbers.

So, It doesn't demonstrate any identity.

Hence, it is an incorrect option.

Hence, option $B$ is the correct answer.