which expression demonstrates the use of the commutative property of addition in the first step of…

which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1 + i)+(21 + 5i)?\n(-1 + i)+(21 + 5i)+0\n-1+(i + 21)+5i\n(-1 + 21)+(i + 5i)\n-(1 - i)+(21 + 5i)

which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1 + i)+(21 + 5i)?\n(-1 + i)+(21 + 5i)+0\n-1+(i + 21)+5i\n(-1 + 21)+(i + 5i)\n-(1 - i)+(21 + 5i)

Answer

Explanation:

Step1: Recall commutative property

The commutative property of addition for real - numbers (a) and (b) is (a + b=b + a). For complex numbers (a+bi) and (c + di), ((a + bi)+(c+di)=(c + di)+(a + bi)). In the expression ((-1 + i)+(21 + 5i)), we can re - arrange the real parts and the imaginary parts separately.

Step2: Analyze each option

  • Option 1: ((-1 + i)+(21 + 5i)+0) just adds 0, not using the commutative property.
  • Option 2: (-1+(i + 21)+5i) is using the associative property of addition ((a + b)+c=a+(b + c)) rather than the commutative property.
  • Option 3: ((-1 + 21)+(i+5i)) uses the commutative property of addition to re - arrange the real parts (-1) and (21) and the imaginary parts (i) and (5i).
  • Option 4: (-(1 - i)+(21 + 5i)) is not related to the commutative property of addition.

Answer:

((-1 + 21)+(i + 5i))