which equation shows an example of the associative property of addition?\n(-4 + i)+4i=-4+(i + 4i)\n(-4 +…

which equation shows an example of the associative property of addition?\n(-4 + i)+4i=-4+(i + 4i)\n(-4 + i)+4i=4i+(-4i + i)\n4i×(-4i + i)=(4i - 4i)+(4i×i)\n(-4i + i)+0=(-4i + i)

which equation shows an example of the associative property of addition?\n(-4 + i)+4i=-4+(i + 4i)\n(-4 + i)+4i=4i+(-4i + i)\n4i×(-4i + i)=(4i - 4i)+(4i×i)\n(-4i + i)+0=(-4i + i)

Answer

Brief Explanations:

The associative property of addition states that for any real or complex numbers (a), (b), and (c), ((a + b)+c=a+(b + c)). In the context of complex - numbers, we check each option.

  • Option 1: ((-4 + i)+4i=-4+(i + 4i)) follows the form ((a + b)+c=a+(b + c)) where (a=-4), (b = i), and (c = 4i).
  • Option 2: ((-4 + i)+4i=4i+(-4i + i)) is a rearrangement of terms which is more related to the commutative property.
  • Option 3: (4i\times(-4i + i)=(4i-4i)+(4i\times i)) involves multiplication and is not an example of the associative property of addition.
  • Option 4: ((-4i + i)+0=(-4i + i)) is an example of the identity property of addition ((a+0 = a)).

Answer:

((-4 + i)+4i=-4+(i + 4i)) (the first option)