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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)

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sqdancefan

The usual rules of addition and multiplication apply to complex numbers as well as to real numbers. The true statements are ...

  • x + y = y + x  . . . . . . . . . . . . . . . commutative property of addition
  • (x × y) × z = x × (y × z) . . . . . . . . associative property of multiplication
  • (x + y) + z = x + (y + z) . . . . . . . . associative property of addition
fichoh

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

  • x + y = y + x
  • (x × y) × z = x × (y × z)
  • (x + y) + z = x + (y + z)

x = a + bi

y = c + di

z = f + gi

Recall :

  • Commutative property establishes that, if the ordering of the numbers an addition or multiplication expression, is changed, the result is unchanged : a + b = b + a

  • The Associative property maintains that, the grouping of values in a multiplication operation does not affe t the result of the product. : a × ( b × c) = b × (a × c) = c × (b × a)

Evaluating the options :

  • x + y = y + x ; This is true (Commutative property of addition)
  • (x × y) × z = x × (y × z) (True according to the Associative property)
  • x - y = y - x (False)
  • (x + y) + z = x + (y + z) (True ; Commutative property)
  • (x – y) – z = x – (y – z) (False)

Hence, only 3 of the given statements are true, according to the Commutative or Associative rule.

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