which equation demonstrates the multiplicative identity property?\n(-3 + 5i)+0=-3 + 5i\n(-3 + 5i)(1)=-3 +…

which equation demonstrates the multiplicative identity property?\n(-3 + 5i)+0=-3 + 5i\n(-3 + 5i)(1)=-3 + 5i\n(-3 + 5i)(-3 + 5i)=-16-30i\n(-3 + 5i)(3 - 5i)=16 + 30i

which equation demonstrates the multiplicative identity property?\n(-3 + 5i)+0=-3 + 5i\n(-3 + 5i)(1)=-3 + 5i\n(-3 + 5i)(-3 + 5i)=-16-30i\n(-3 + 5i)(3 - 5i)=16 + 30i

Answer

Explanation:

Step1: Recall multiplicative identity property

The multiplicative - identity property states that for any number (a), (a\times1 = a). In the context of complex numbers, if (z=a + bi) is a complex number, then (z\times1=(a + bi)\times1=a + bi).

Step2: Analyze each option

  • Option 1: ((-3 + 5i)+0=-3 + 5i) shows the additive - identity property ((a+0 = a)).
  • Option 2: ((-3 + 5i)(1)=-3 + 5i) follows the multiplicative - identity property for complex numbers.
  • Option 3: ((-3 + 5i)(-3 + 5i)=(-3)^2+2\times(-3)\times(5i)+(5i)^2=9-30i - 25=-16-30i) is the square of a complex number.
  • Option 4: ((-3 + 5i)(3 - 5i)=-9 + 15i+15i-25i^2=-9 + 30i + 25=16 + 30i) is the product of two complex conjugates.

Answer:

((-3 + 5i)(1)=-3 + 5i) (the second option)