Jaden Bird

Answered

2022-11-30

Which equation illustrates the identity property of multiplication? A$(a+\mathrm{bi})\times c=(\mathrm{ac}+\mathrm{bci})$ B$(a+\mathrm{bi})\times 0=0$ C$(a+\mathrm{bi})\times (c+\mathrm{di})=(c+\mathrm{di})\times (a+\mathrm{bi})$ D$(a+\mathrm{bi})\times 1=(a+\mathrm{bi})$

Answer & Explanation

marystevensbUS

Expert

2022-12-01Added 9 answers

$(a+\mathrm{bi})\times 1=(a+\mathrm{bi})$

Step-1: Explanation for correct answer:

For option (D): $(a+\mathrm{bi})\times 1=(a+\mathrm{bi})$

We know that the identity property of multiplication states that when a number $A$ is multiplied by $1$the product is the number itself.

i.e., $A\times 1=A$

In option $\left(D\right)$, $A=\left(a+\mathrm{bi}\right)$

Therefore, the identity property of multiplication is represented by $(a+\mathrm{bi})\times 1=(a+\mathrm{bi})$

Step-2: Explanation for incorrect answer.

For option (A):$(a+\mathrm{bi})\times c=(\mathrm{ac}+\mathrm{bci})$

As, $(a+\mathrm{bi})\ne (\mathrm{ac}+\mathrm{bci})$

Thus, it is not of the form $A\times 1=A$ [ The identity property of multiplication ]

For option (B):$(a+\mathrm{bi})\times 0=0$

As, $(a+\mathrm{bi})\ne 0$ and $1\ne 0$

Thus, it is not of the form $A\times 1=A$ [ The identity property of multiplication ]

For option (C):$(a+\mathrm{bi})\times (c+\mathrm{di})=(c+\mathrm{di})\times (a+\mathrm{bi})$

As, $(a+\mathrm{bi})\ne 1$ and $(c+\mathrm{di})\ne 1$

Thus, it is not of the form $A\times 1=A$ [ The identity property of multiplication ]

So, all these options does not verify the identity property of multiplication.

Hence, the correct option is $\left(D\right)$.

Step-1: Explanation for correct answer:

For option (D): $(a+\mathrm{bi})\times 1=(a+\mathrm{bi})$

We know that the identity property of multiplication states that when a number $A$ is multiplied by $1$the product is the number itself.

i.e., $A\times 1=A$

In option $\left(D\right)$, $A=\left(a+\mathrm{bi}\right)$

Therefore, the identity property of multiplication is represented by $(a+\mathrm{bi})\times 1=(a+\mathrm{bi})$

Step-2: Explanation for incorrect answer.

For option (A):$(a+\mathrm{bi})\times c=(\mathrm{ac}+\mathrm{bci})$

As, $(a+\mathrm{bi})\ne (\mathrm{ac}+\mathrm{bci})$

Thus, it is not of the form $A\times 1=A$ [ The identity property of multiplication ]

For option (B):$(a+\mathrm{bi})\times 0=0$

As, $(a+\mathrm{bi})\ne 0$ and $1\ne 0$

Thus, it is not of the form $A\times 1=A$ [ The identity property of multiplication ]

For option (C):$(a+\mathrm{bi})\times (c+\mathrm{di})=(c+\mathrm{di})\times (a+\mathrm{bi})$

As, $(a+\mathrm{bi})\ne 1$ and $(c+\mathrm{di})\ne 1$

Thus, it is not of the form $A\times 1=A$ [ The identity property of multiplication ]

So, all these options does not verify the identity property of multiplication.

Hence, the correct option is $\left(D\right)$.

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