Question

Let x = a + bi and y = c + di and z = f + gi. Which statements are true? check all of the boxes that apply. X + y = y + x (x × y) × z = x × (y × z) x – y = y – x (x + y) + z = x + (y + z) (x – y) – z = x – (y – z).

Answer 1

The true statements after evaluating the expression based on principle of commutativity and associativity are :

A: x + y = y + x

B; (x × y) × z = x × (y × z)

D: (x + y) + z = x + (y + z)

We are given;

x = a + bi

y = c + di

z = f + gi

Now according to properties of algebra, we know that;

• Commutative property states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. For example; a + b = b + a

• The Associative property states that; a × ( b × c) = b × (a × c) = c × (b × a)

Looking at the options :

A) x + y = y + x ; This is true as it follows Commutative property of addition

B) (x × y) × z = x × (y × z) ; This is true as it follows the Associative property.

C) x - y = y - x ; this is false as it does not follow both properties.

D) (x + y) + z = x + (y + z) ; This is true as it follows the Commutative property.

E) (x – y) – z = x – (y – z) ; This is False as it does not follow any of the 2 properties.

Read more on Associative and commutative properties at; brainly.com/question/549862