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)

$(a+\mathrm{bi})\times 1=(a+\mathrm{bi})$
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 $\left(D\right)$.