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)

x + y = y + x … … … True, since addition is commutative.

(x • y) • z = x • (y • z) … … … True, since multiplication is associative.

x - y = y - x … … … False. Suppose y = 0. Then the claim is x = -x, which is only true if x = 0.

(x + y) + z = x + (y + z) … … … True, since addition is associative.

(x - y) - z = x - (y - z) … … … False. If x = y = 0, then the claim is -z = z, which only holds for z = 0.

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4

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