Which equation is an example of the commutative property of multiplication? (4 + 2i) = (2i + 4) (4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i) (4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)(1) (4 + 2i) = (4 + 2i + 0)

If we alternate the order of the numbers we're multiplying, the product does not change, this is the commutative property of multiplication

Considering two real numbers a and b, the commutative property of multiplication of these two numbers will show: ⇒ a × b = b × a
Complex number (a + bi) also shows the commutative property of multiplication. ⇒ (a + bi) = (bi + a)

In the first option, it is given that:

(4 + 2i) = (2i + 4)

In this we can see that there is no multiplication between two complex numbers instead, it shows the addition. Hence this shows the commutative property of addition.

In the third option, it is given that:

(4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)

Here we can see that there is multiplication between the two complex numbers but the order of multiplication is same on both the sides, hence this does not show the commutative property of multiplication.

In the fourth option, it is given that:

(4 + 2i) = (4 + 2i + 0)

We can clearly see there is no multiplication in this equation, hence this does not follow the commutative property of multiplication.

In the second option, it is given that:

(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)

Here we can see that, there is multiplication between two complex numbers and the order of multiplication is also different on one side, this clearly follows the commutative property of multiplication.

Therefore, the second option i.e. (4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i) is the correct example of the commutative property of multiplication.

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