Question

which equation demonstrates the additive identity property?
○ (7 + 4i) + (7 - 4i) = 14
○ (7 + 4i) + 0 = 7 + 4i
○ (7 + 4i)(1) = 7 + 4i
○ (7 + 4i) + (-7 - 4i) = 0

Explanation:

Step1: Recall Additive Identity

The additive identity property states that for any number \( a \), \( a + 0 = a \).

Step2: Analyze Each Option

• Option 1: \( (7 + 4i)+(7 - 4i)=14 \) is adding a complex number and its conjugate, not using additive identity.
• Option 2: \( (7 + 4i)+0 = 7 + 4i \) matches \( a + 0 = a \) (here \( a = 7 + 4i \)).
• Option 3: \( (7 + 4i)(1)=7 + 4i \) is multiplicative identity (multiplying by 1), not additive.
• Option 4: \( (7 + 4i)+(-7 - 4i)=0 \) is adding a number and its additive inverse, not identity.

Answer:

\((7 + 4i)+0 = 7 + 4i\) (the second option)