Which property of multiplication is shown below? If x = a + bi and y = c + di, x × y = y × x. . .
Commutative property, Identity property, Distributive property, Associative property

Solution:

The commutative property of multiplication says that a change in the order of the number does not change the product of the number.

If x = a + ib and y = c + id, then x × y = y × x.

Example: Let x = 5 + 3i and y = 2 + 6i

Let us multiply the complex conjugates.

LHS = x × y = (5 + 3i ) × (2 + 6i)

= 10 + 15i + 6i + 18i2

= 10 + 30i + 6i + 18(- 1) [As we know that i2 = -1]

= - 8 + 36i

RHS = y × x = (2 + 6i) × (5 + 3i )

= 10 + 6i + 30i + 18i2

= 10 + 6i + 30i + 18(- 1)

= - 8 + 36i

LHS = RHS

Thus, the commutative property of multiplication is shown in the statement.

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Which property of multiplication is shown below? If x = a + bi and y = c + di, x × y = y × x. . .
Commutative property, Identity property, Distributive property, Associative property

Summary:

The property of multiplication shown in the above statement is the commutative property of multiplication.