Which equation illustrates the identity property of multiplication? A(a+bi)×c=(ac+bci) B(a+bi)×0=0 C(a+bi)×(c+di)=(c+di)×(a+bi) D(a+bi)×1=(a+bi)

Jaden Bird

Jaden Bird

Answered

2022-11-30

Which equation illustrates the identity property of multiplication? A(a+bi)×c=(ac+bci) B(a+bi)×0=0 C(a+bi)×(c+di)=(c+di)×(a+bi) D(a+bi)×1=(a+bi)

Answer & Explanation

marystevensbUS

marystevensbUS

Expert

2022-12-01Added 9 answers

(a+bi)×1=(a+bi)
Step-1: Explanation for correct answer:
For option (D): (a+bi)×1=(a+bi)
We know that the identity property of multiplication states that when a number A is multiplied by 1the product is the number itself.
i.e., A×1=A
In option (D), A=a+bi
Therefore, the identity property of multiplication is represented by (a+bi)×1=(a+bi)
Step-2: Explanation for incorrect answer.
For option (A):(a+bi)×c=(ac+bci)
As, (a+bi)(ac+bci)
Thus, it is not of the form A×1=A [ The identity property of multiplication ]
For option (B):(a+bi)×0=0
As, (a+bi)0 and 10
Thus, it is not of the form A×1=A [ The identity property of multiplication ]
For option (C):(a+bi)×(c+di)=(c+di)×(a+bi)
As, (a+bi)1 and (c+di)1
Thus, it is not of the form A×1=A [ The identity property of multiplication ]
So, all these options does not verify the identity property of multiplication.
Hence, the correct option is (D).

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