Question

Which property of multiplication is shown below?

If x = a + bi and y = c + di, x × y = y × x.

Answer 1

Explanation:

The given values of x and y are:

`x=a+bi` and
`y=c+di`

Then, using the commutative property which states that it is a binary operation in which ab=ba whenever you change the order of the operands.

Therefore,
`xy=yx`

`(a+bi)(c+di)=(c+di)(a+bi)`

`ac+bci+adi+bdi^2=ca+dai+cbi+dbi^2`

`ac+(bc+ad)i-bd=ca+(da+cb)i-db`

Thus, commutative property of multiplication is as shown above.

Answer 2

There are four properties of multiplication namely commutative, associative, multiplicative identity and distributive. The equation given defines the commutative property of multiplication where two numbers are multiplied, the product will still be the same no matter what is the order of the multiplicands.