The property of multiplication illustrated in the statement is the Commutative Property.
This property states that changing the order of the factors does not change the product. In simpler terms, for any two numbers x and y, the equation x × y = y × x holds true. In the context of the question, using complex numbers (where x = a + bi and y = c + di), the same principle applies: the product remains the same regardless of the order in which you multiply x and y.
To further clarify, let’s consider an example. If we take specific values for x and y, say x = 2 + 3i and y = 4 + 5i, we can compute the products:
- x × y = (2 + 3i)(4 + 5i) = 8 + 10i + 12i + 15i² = 8 + 22i – 15 = -7 + 22i
- y × x = (4 + 5i)(2 + 3i) = 8 + 12i + 10i + 15i² = 8 + 22i – 15 = -7 + 22i
As we see, x × y equals y × x, confirming that the commutative property holds for these complex numbers as well.